Bibliography

for

Newton's Method

Return to Numerical Methods - Numerical Analysis

 

  1. On a theorem of L.V. Kantorovich concerning Newton's method
    Argyros I.K.
    Journal of Computational and Applied Mathematics, 15 June 2003, vol. 155, no. 2, pp. 223-230(8), Ingenta.  
  2. Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P0 Function
    Huang Z.H.; Han J.; Chen Z.
    Journal of Optimization Theory and Applications, April 2003, vol. 117, no. 1, pp. 39-68(30), Ingenta.  
  3. The Inexact Newton-Like Method for Inverse Eigenvalue Problem
    Chan R.H.; Chung H.L.; Xu S.-F.
    Bit Numerical Mathematics, March 2003, vol. 43, no. 1, pp. 7-20(14), Ingenta.  
  4. Structured Secant Method Based on a New Quasi-Newton Equation for Nonlinear Least Squares Problems
    Zhang J.Z.; Xue Y.; Zhang K.
    Bit Numerical Mathematics, March 2003, vol. 43, no. 1, pp. 217-229(13), Ingenta.  
  5. A penalty/Newton/conjugate gradient method for the solution of obstacle problems
    Glowinski R.; Kuznetsov Y.A.; Pan T.-W.
    Comptes Rendus Mathematique, 1 March 2003, vol. 336, no. 5, pp. 435-440(6), Ingenta.  
  6. Global Linear and Quadratic One-step Smoothing Newton Method for P0-LCP
    Zhang L.; Zhang X.
    Journal of Global Optimization, April 2003, vol. 25, no. 4, pp. 363-376(14), Ingenta.  
  7. Some variant of Newton's method with third-order convergence
    Frontini M.; Sormani E.
    Applied Mathematics and Computation, 10 August 2003, vol. 140, no. 2, pp. 419-426(8), Ingenta.  
  8. The Newton-arithmetic mean method for the solution of systems of nonlinear equations
    Galligani E.
    Applied Mathematics and Computation, 10 January 2003, vol. 134, no. 1, pp. 9-34(26), Ingenta.  
  9. Simultaneous Point Estimates for Newton's Method
    Batra P.
    Bit Numerical Mathematics, 2002, vol. 42, no. 3, pp. 467-476(10), Ingenta.  
  10. Modified Newton method for reactive dispatching
    da Costa G.R.M.
    International Journal of Electrical Power and Energy Systems, December 2002, vol. 24, no. 10, pp. 815-819(5), Ingenta.  
  11. Solving a Boundary Value Problem by a Newton-Like Method
    Ezquerro J.A.; Herna´ndez M.A.; Salanova M.A.
    International Journal of Computer Mathematics, 1 January 2002, vol. 79, no. 10, pp. 1113-1120(8), Ingenta.  
  12. Iteratively regularized Gauss-Newton method for atmospheric remote sensing
    Doicu A.; Schreier F.; Hess M.
    Computer Physics Communications, 15 October 2002, vol. 148, no. 2, pp. 214-226(13), Ingenta.  
  13. The Geometry of the Newton Method on Non-Compact Lie Groups
    Mahony R.; Manton J.H.
    Journal of Global Optimization, August 2002, vol. 23, no. 3-4, pp. 309-327(19), Ingenta.  
  14. On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method
    Farhat C.; Tezaur R.; Djellouli R.
    Inverse Problems, 2002, vol. 18, no. 5, pp. 1229-1246(18), Ingenta.  
  15. On the Gauss--Newton method for l1 orthogonal distance regression
    Watson G.A.
    IMA Journal of Numerical Analysis, July 2002, vol. 22, no. 3, pp. 345-357(13), Ingenta.  
  16. Dynamics of Newton's method for solving some equations
    Jeong M.; Ok Kim G.; Kim S.
    Computers and Graphics, April 2002, vol. 26, no. 2, pp. 271-279(9), Ingenta.  
  17. A Globally Convergent Smoothing Newton Method for Nonsmooth Equations and Its Application to Complementarity Problems
    Taji K.; Miyamoto M.
    Computational Optimization and Applications, April 2002, vol. 22, no. 1, pp. 81-101(21), Ingenta.  
  18. Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems
    Qi L.; Sun D.
    Journal of Optimization Theory and Applications, April 2002, vol. 113, no. 1, pp. 121-147(27), Ingenta.  
  19. Modelling the three-way catalytic converter with mechanistic kinetics using the Newton-Krylov method on a parallel computer
    Mukadi L.S.; Hayes R.E.
    Computers and Chemical Engineering, 15 March 2002, vol. 26, no. 3, pp. 439-455(17), Ingenta.  
  20. Bifurcation analysis of incompressible flow in a driven cavity by the Newton-Picard method
    Tiesinga G.; Wubs F.W.; Veldman A.E.P.
    Journal of Computational and Applied Mathematics, 1 March 2002, vol. 140, no. 1, pp. 751-772(22), Ingenta.  
  21. Kepler equation and accelerated Newton method
    Palacios M.
    Journal of Computational and Applied Mathematics, 15 January 2002, vol. 138, no. 2, pp. 335-346(12), Ingenta.  
  22. A direct Newton method for calculus of variations
    Levin1 Y.; Nediak M.; Ben-Israel A.
    Journal of Computational and Applied Mathematics, 15 February 2002, vol. 139, no. 2, pp. 197-213(17), Ingenta.  
  23. Newton-Raphson Method and Stability of Nonlinear Information Image-Recovery Techniques
    Bajkova A.T.
    Radiophysics and Quantum Electronics, October 2001, vol. 43, no. 10, pp. 805-816(12), Ingenta.  
  24. A Newton method for systems of m equations in n variables
    Levin Y.; Ben-Israel A.
    Nonlinear Analysis, August 2001, vol. 47, no. 3, pp. 1961-1971(11), Ingenta.  
  25. An acceleration of Newton's method: Super-Halley method
    Gutierrez J.M.; Hernandez M.A.
    Applied Mathematics and Computation, 25 January 2001, vol. 117, no. 2, pp. 223-239(17), Ingenta.  
  26. Modified Newton and secant methods for solving an order O([Graphics:../Images/Newton'sMethodBib_gr_1.gif]) finite-difference problem  
    Lin, Zhenghua; Yu, Xiaolin; Sheng, Zhongping  
    Ann. Differential Equations 16 (2000), no. 2, 134--144, Math. Sci. Net.   
  27. Variable dimension Newton-Raphson method  
    Ng, S. W.; Lee, Y. S.  
    IEEE Trans. Circuits Systems I Fund. Theory Appl. 47 (2000), no. 6, 809--817, Math. Sci. Net.   
  28. Newton's Method in Shape Optimisation: A Three-Dimensional Case
    Novruzi A.; Roche J.R.
    Bit Numerical Mathematics, 2000, vol. 40, no. 1, pp. 102-120(19), Ingenta.  
  29. Theoretical Efficiency of an Inexact Newton Method
    Deng N.Y.; Wang Z.Z.
    Journal of Optimization Theory and Applications, April 2000, vol. 105, no. 1, pp. 97-112(16), Ingenta.  
  30. A Variant of Newton's Method with Accelerated Third-Order Convergence
    Weerakoon S.; Fernando T.G.I.
    Applied Mathematics Letters, November 2000, vol. 13, no. 8, pp. 87-93(7), Ingenta.  
  31. Newton's Method for Zero Points of a Matrix Function and its Applications to Queueing Models
    Nishimura S.; Harashima A.
    Journal of the Operations Research Society of Japan, September 2000, vol. 43, no. 3, pp. 396-416(21), Ingenta.  
  32. The theory of Newton's method
    Galantai A.
    Journal of Computational and Applied Mathematics, 1 December 2000, vol. 124, no. 1, pp. 25-44(20), Ingenta.  
  33. Improved Newton method for optimal power flow problem
    da Costa G.R.M.; Costa C.E.U.
    International Journal of Electrical Power and Energy Systems, 1 October 2000, vol. 22, no. 7, pp. 459-462(4), Ingenta.  
  34. Construction of the Jordan decomposition by means of Newton's method
    Schmidt D.
    Linear Algebra and its Applications, 15 July 2000, vol. 314, no. 1, pp. 75-89(15), Ingenta.  
  35. A new continuation Newton-like method and its deformation
    Wu X.-Y.
    Applied Mathematics and Computation, 1 June 2000, vol. 112, no. 1, pp. 75-78(4), Ingenta.  
  36. Newton's method and generation of a determinantal family of iteration functions
    Kalantari B.; Gerlach J.
    Journal of Computational and Applied Mathematics, 1 April 2000, vol. 116, no. 1, pp. 195-200(6), Ingenta.  
  37. From Square Roots to n-th Roots: Newton's Method in Disguise
    W. M. Priestley    
    College Math Journal: Volume 30, Number 5, (1999), Pages: 387-388.
  38. Computing Square Roots Fast: Illustrating the Cubic Order of Convergence  
    John Mathews; Russell Howell  
    International Journal of Mathematics Education in Science and Technology, 1999, Vol. 30, No. 2, pp. 289-293.  
  39. The application of Julia set to Newton-secants method  
    Tomova, Anna  
    Applications of mathematics in engineering and economics (Sozopol, 1999), 94--95, Heron Press, Sofia, 2000, Math. Sci. Net.  
  40. Newton maps: fractals from Newton's method for the circle map
    Cartwright J.H.E.
    Computers and Graphics, August 1999, vol. 23, no. 4, pp. 607-612(6), Ingenta.  
  41. A Newton method for three-dimensional fretting problems
    Stromberg N.
    International Journal of Solids and Structures, 1 May 1999, vol. 36, no. 14, pp. 2075-2090(16), Ingenta.  
  42. A practical choice of parameters in improved SOR-Newton method with orderings
    Ishiwata E.
    Journal of Computational and Applied Mathematics, 26 February 1999, vol. 102, no. 2, pp. 315-331(17), Ingenta.  
  43. Numerical solutions for orthogonal wavelet filters by Newton method
    Chang L.-W.; Shen Y.-E.
    Signal Processing: Image Communication, August 1999, vol. 14, no. 10, pp. 879-887(9), Ingenta.  
  44. Application of Galerkin Finite-Element Method with Newton Iterations in Computing Steady-State Solutions of Unipolar Charge Currents in Corona Devices
    Feng J.Q.
    Journal of Computational Physics, May 1999, vol. 151, no. 2, pp. 969-989(21), Ingenta.  
  45. Strong consistency of robust nonlinear regression estimates using Newton-Raphson algorithms. (Chinese)
    Yuan, Jun Zhu
    J. Baoji College Arts Sci. Nat. Sci. 19 (1999), no. 4, 50--53, Math. Sci. Net.  
  46. Variations on a Theme of Newton  
    Robert M. Corless  
    Mathematics Magazine: Volume 29, Number 1, (1998), Pages: 34-41.  
  47. The Newton and Halley Methods for Complex Roots  
    Lily Yau and Adi Ben-Israel  
    American Mathematical Monthly, Vol. 105, No. 9, (November, 1998), pp. 806-818, Jstor.  
  48. A global Newton method for the zeros of cylinder functions
    Segura J.
    Numerical Algorithms, 1998, vol. 18, no. 3/4, pp. 259-276(18), Ingenta.  
  49. A parallel quasi-Newton method for Gaussian data fitting
    Caprioli P.; Holmes M.H.
    Parallel Computing, October 1998, vol. 24, no. 11, pp. 1635-1651(17), Ingenta.  
  50. A statistically-based Newton method for pose refinement
    Pece A.; Worrall A.
    Image and Vision Computing, June 1998, vol. 16, no. 8, pp. 541-544(4), Ingenta.  
  51. nth Root extraction: Double iteration process and Newton's method
    Dubeau F.
    Journal of Computational and Applied Mathematics, 4 May 1998, vol. 91, no. 2, pp. 191-198(8), Ingenta.  
  52. A generalization of the Newton-Raphson method. (Japanese)   
    Fukushima, Katsuhiko; Kitagawa, Seinosuke
    Sugaku 50 (1998), no. 2, 211--214, Math. Sci. Net.  
  53. A Continuous Version of Newton's Method
    Steve Hetzler
    College Math Journal: Volume 28, Number 5, (1997), Pages: 348-35.
  54. An Inexact Newton Method for Systems Arising from the Finite Element Method
    Capon P.J.; Jimack P.K.
    Applied Mathematics Letters, May 1997, vol. 10, no. 3, pp. 9-12(4), Ingenta.  
  55. An improvement of convergence in Newton's method
    Lopez S.
    Computer Methods in Applied Mechanics and Engineering, 30 June 1997, vol. 145, no. 3, pp. 323-327(5), Ingenta.  
  56. Accelerated Convergence in Newton's Method (in Classroom Notes)  
    William F. Ford, James A. Pennline  
    SIAM Review, Vol. 38, No. 4. (Dec., 1996), pp. 658-659, Jstor.  
  57. Newton's Method for Resolving Affected Equations  
    Chris Christenson
    College Math Journal: Volume 27, Number 5, (1996), Pages: 330-340.
  58. An example of the secant method of iterative approximation in a fifteenth-century Sanskrit text  
    Plofker, Kim  
    Historia Math. 23 (1996), no. 3, 246--256, Math. Sci. Net.  
  59. A Newton method for solving the inverse scattering problem for a sound-hard obstacle
    Mnch L.
    Inverse Problems, 1996, vol. 12, no. 3, pp. 309-323(15), Ingenta.  
  60. A Stepsize Control for the Botsaris-Newton Method
    Sturm T.F.
    Journal of Mathematical Analysis and Applications, April 1996, vol. 199, no. 1, pp. 59-74(16), Ingenta.  
  61. The Dynamics of Newton's Methos for Cubic Polynomials  
    James A. Walsh   
    College Math Journal: Volume 26, Number 1, (1995), Pages: 22-27.  
  62. On the Geometry of Halley's Method  
    T. R. Scavo, J. B. Thoo  
    American Mathematical Monthly, Vol. 102, No. 5. (May, 1995), pp. 417-426, Jstor.  
  63. Historical Development of the Newton-Raphson Method  
    Tjalling J. Ypma  
    SIAM Review, Vol. 37, No. 4. (Dec., 1995), pp. 531-551, Jstor.  
  64. Average-Case Optimality of a Hybrid Secant-Bisection Method  
    Erich Novak, Klaus Ritter, Henryk Wozniakowski  
    Mathematics of Computation, Vol. 64, No. 212. (Oct., 1995), pp. 1517-1539, Jstor  
  65. A generalized Newton-Raphson method using curvature  
    Lee, In-Won; Jung, Gil-Ho
    Comm. Numer. Methods Engrg. 11 (1995), no. 9, 757--763, Math. Sci. Net.  
  66. Newton Raphson method, scaling at fractal boundaries and Mathematica   
    Bisoi, A. K.
    Math. Comput. Modelling 21 (1995), no. 10, 91--102, Math. Sci. Net.  
  67. Remarks on the convergence of the Newton-Raphson method  
    Berinde, Vasile
    Rev. Anal. Numér. Théor. Approx. 24 (1995), no. 1-2, 15--21, Math. Sci. Net.   
  68. Historical Development of the Newton-Raphson Method  
    Tjalling J. Ypma  
    SIAM Review, Vol. 37, No. 4. (Dec., 1995), pp. 531-551, Jstor.  
  69. Approximate Zeros of Quadratically Convergent Algorithms  
    Pengyuan Chen  
    Mathematics of Computation, Vol. 63, No. 207. (Jul., 1994), pp. 247-270, Jstor.  
  70. Accelerated Convergence in Newton's Method (in Classroom Notes)  
    Jurgen Gerlach  
    SIAM Review, Vol. 36, No. 2. (Jun., 1994), pp. 272-276, Jstor.  
  71. Combining binary search and Newton's method to compute real roots for a class of real functions.    
    Ye, Yinyu    
    J. Complexity 10 (1994), no. 3, 271--280, MathSciNet.  
  72. Pathological Functions for Newton's Method  
    George C. Donovan, Arnold R. Miller, Timothy J. Moreland  
    American Mathematical Monthly, Vol. 100, No. 1. (Jan., 1993), pp. 53-58, Jstor.  
  73. The Secant Method and the Golden Mean (in Notes)  
    Melvin J. Maron, Robert J. Lopez  
    American Mathematical Monthly, Vol. 100, No. 7. (Aug. - Sep., 1993), pp. 676-678, Jstor.  
  74. Using the Secant Method to Approximate the Roots of an Equation  
    Peter Lochiel Glidden  
    School Science and Mathematics, Vol. 93, No. 1, (1993), pp. 5-8.  
  75. On the Superlinear Convergence of the Secant Method  
    Marco Vianello, Renato Zanovello  
    American Mathematical Monthly, Vol. 99, No. 8. (Oct., 1992), pp. 758-761, Jstor  
  76. Newton-Raphson's method and convexity  
    Hernández Verón, Miguel A.
    Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 22 (1992), no. 1, 159--166, Math. Sci. Net.   
  77. A combined method for polynomial roots using modified Newton-Raphson with minimum searching  
    Lynge, Walter C.
    J. Comput. Appl. Math. 42 (1992), no. 3, 339--355, Math. Sci. Net.   
  78. The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations  
    Roger Alexander  
    Mathematics of Computation, Vol. 57, No. 196. (Oct., 1991), pp. 673-701, Jstor.  
  79. Convergence of the Newton-Raphson algorithm in elastic-plastic incremental analysis
    Caddemi, S.; Martin, J. B.  
    Internat. J. Numer. Methods Engrg. 31 (1991), no. 1, 177--191, Math. Sci. Net.   
  80. On the Newton-Raphson iterative method for the computation of the square root  
    Badea, C at alin; Buze teanu,  Serban N.
    An. Univ. Bucurec sti Mat. Inform. 39/40 (1990/1991), no. 3, 3--13, Math. Sci. Net.  
  81. A Gauss-Newton Method for Nonlinear Regression   
    M. N. Ediger, Food and Drug Administration  
    The Mathematica Journal, Vol. 1, No. 2, (Fall 1990), pp 42-44.   
  82. On the R-Order of Newton-Like Methods for Enclosing Solutions of Nonlinear Equations  
    Andreas Frommer, Gunter Mayer  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 1. (Feb., 1990), pp. 105-116, Jstor.  
  83. A parabolic extension of Newton's method   
    Sheldon P. Gordon  and  Ellis R. Von Eschen  
    Int. J. Math. Educ. Sci. Technol.,Vol. 21, No. 4, (1990), pp. 519-525.
  84. Convergence of the Newton-Raphson method for boundary value problems of ordinary differential equations  
    Guenther, Ronald B.; Lee, John W.
    Computational solution of nonlinear systems of equations (Fort Collins, CO, 1988), 257--264, Lectures in Appl. Math., 26, Amer. Math. Soc., Providence, RI, (1990), Math. Sci. Net.   
  85. Newton-Raphson behaving chaotically  
    Robin, A. C.
    Bull. Inst. Math. Appl. 26 (1990), no. 3, 34--35, Math. Sci. Net.   
  86. An Improved Newton's Method  
    John Mathews  
    The AMATYC Review, Vol. 10, No. 2, (Spring, 1989), pp. 9-14.  
  87. On Halley-Like Algorithms for Simultaneous Approximation of Polynomial Complex Zeros  
    Miodrag S. Petkovic  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 3. (Jun., 1989), pp. 740-763, Jstor.  
  88. An Approximate Newton Method for the Solution of the Basic Semiconductor Device Equations  
    C. Ringhofer; C. Schmeiser  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 3. (Jun., 1989), pp. 507-516, Jstor.  
  89. An asynchronous Newton-Raphson method  
    Lootsma, Freerk A.
    Supercomputing (Trondheim, 1989), 367--376, NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., 62, Springer, Berlin, 1989, Math. Sci. Net.  
  90. Gauss-Newton versus Newton-Raphson algorithm for the recursive generalized least-squares identification  
    Weinfeld, Roman; Unton, Fryderyk Z.
    Control Cybernet. 18 (1989), no. 2, 171--178, Math. Sci. Net.   
  91. The Projected Newton Method has Order 1 + 2^1/2 for the Symmetric Eigenvalue Problem
    R. A. Tapia; David L. Whitley
    SIAM Journal on Numerical Analysis, Vol. 25, No. 6. (Dec., 1988), pp. 1376-1382, Jstor.  
  92. A Pointwise Quasi-Newton Method for Integral Equations  
    C. T. Kelley; J. I. Northrup  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 5. (Oct., 1988), pp. 1138-1155, Jstor.  
  93. Newton's nth Root Method Without Derivatives
    David A. Smith  
    College Math Journal: Volume 18, Number 5, (1987), Pages: 403-406.  
  94. Complex Roots of Polynomials by Newton-Raphson Method   
    R. D. Murphy  
    Journal of Computers in Mathematics and Science Teaching, (1987),  pp. 44-45.  
  95. A Quasi-Newton Method for Elliptic Boundary Value Problems
    C. T. Kelley; E. W. Sachs  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 3. (Jun., 1987), pp. 516-531, Jstor.  
  96. A Nonmonotone Line Search Technique for Newton's Method  
    L. Grippo, F. Lampariello, S. Lucidi  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 4. (Aug., 1986), pp. 707-716, Jstor.  
  97. Newton's Method and the Jenkins-Traub Algorithm  
    R. N. Pederson  
    Proceedings of the American Mathematical Society, Vol. 97, No. 4. (Aug., 1986), pp. 687-690, Jstor.  
  98. Attracting Orbits in Newton's Method  
    Mike Hurley  
    Transactions of the American Mathematical Society, Vol. 297, No. 1. (Sep., 1986), pp.143-158, Jstor.  
  99. Newton's Method for the Matrix Square Root  
    Nicholas J. Higham  
    Mathematics of Computation, Vol. 46, No. 174. (Apr., 1986), pp. 537-549, Jstor.  
  100. Complex Roots: The Bairstow-Hitchcock Method  
    Clark Kimberling  
    The Mathematics Teacher, Vol. 79, No. 4, (April, 1986), pp. 278-282.  
  101. Pitfalls in the Use of Computers for the Newton-Raphson Method  
    D. Mackie  and  T. Scott  
    The Mathematical Gazette, Vol. 69, no. 450, (Dec., 1985), pp. 252-257.  
  102. Newton-Raphson in reverse  
    Davies, M.  
    Math. Student 47 (1979), no. 2-4, 149--150 (1985), Math. Sci. Net.  
  103. On Halley's Iteration Method (in Notes)  
    Walter Gander  
    American Mathematical Monthly, Vol. 92, No. 2. (Feb., 1985), pp. 131-134, Jstor.  
  104. Orthogonal Projections on Convex Sets for Newton-Like Methods  
    Stanislaw M. Grzegorski  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 6. (Dec., 1985), pp. 1208-1219, Jstor.  
  105. An Approximate Newton Method for Coupled Nonlinear Systems  
    Tony F. Chan  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 5. (Oct., 1985), pp. 904-913, Jstor.  
  106. Global analysis of continuous analogues of the Levenberg-Marquardt and Newton-Raphson methods for solving nonlinear equations  
    Tanabe, Kunio
    Ann. Inst. Statist. Math. 37 (1985), no. 1, 189--203, Math. Sci. Net.   
  107. Convergence of Newton Method in Nonlinear Network Analysis
    Altman T.; Boulos P.F.
    Mathematical and Computer Modelling, February 1995, vol. 21, no. 4, pp. 35-41(7), Ingenta.  
  108. Newton Raphson Method, Scaling at Fractal Boundaries and Mathematica
    Bisoi A.K.
    Mathematical and Computer Modelling, May 1995, vol. 21, no. 10, pp. 91-102(12, Ingenta.  
  109. A generalization of Newton Raphson  
    MacLeod, Allan J.
    Internat. J. Math. Ed. Sci. Tech. 15 (1984), no. 1, 117--120, Math. Sci. Net.   
  110. Newton's Method and Symbolic Dynamics  
    Sherman Wong  
    Proceedings of the American Mathematical Society, Vol. 91, No. 2. (Jun., 1984), pp. 245-253, Jstor.  
  111. On the Convergence of some Interval-Arithmetic Modifications of Newton's Method  
    G. Alefeld  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 2. (Apr., 1984), pp. 363-372, Jstor.  
  112. Newton's Method, Circle Maps, and Chaotic Motion  
    Donald G. Saari, John B. Urenko  
    American Mathematical Monthly, Vol. 91, No. 1. (Jan., 1984), pp. 3-17, Jstor.  
  113. Aitken Sequences and Fibonacci Numbers  
    G. M. Phillips  
    American Mathematical Monthly, Vol. 91, No. 6. (Jun. - Jul., 1984), pp. 354-357, Jstor.  
  114. Newton-Type Minimization Via the Lanczos Method  
    Stephen G. Nash  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 770-788, Jstor.  
  115. On the Local Convergence of a Quasi-Newton Method for the Nonlinear Programming Problem  
    Thomas F. Coleman; Andrew R. Conn  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 755-769, Jstor.    
  116. A Nonconverging Newton Sequence  
    Peter Petek  
    Mathematics Magazine: Volume 14, Number 1, (1983), Pages: 43-45.  
  117. A New Acceleration Method for Newton's Method at Singular Points  
    C. T. Kelley, R. Suresh  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 5. (Oct., 1983), pp. 1001-1009, Jstor.  
  118. Convergence Rates for Newton's Method at Singular Points  
    D. W. Decker, H. B. Keller, C. T. Kelley  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 2. (Apr., 1983), pp. 296-314, Jstor.  
  119. Analysis of Newton's Method at Irregular Singularities  
    A. Griewank, M. R. Osborne  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 4. (Aug., 1983), pp. 747-773, Jstor.  
  120. Local Convergence of Difference Newton-Like Methods  
    T. J. Ypma  
    Mathematics of Computation, Vol. 41, No. 164. (Oct., 1983), pp. 527-536, Jstor.  
  121. Finding a Multiple Zero by Transformations and Newton-Like Methods  
    T. J. Ypma  
    SIAM Review, Vol. 25, No. 3. (Jul., 1983), pp. 365-378, Jstor.  
  122. A Quasi-Newton Method Employing Direct Secant Updates of Matrix Factorizations  
    George W. Johnson; Nieves H. Austria  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 2. (Apr., 1983), pp. 315-325, Jstor.  
  123. Newton's Method with a Model Trust Region Modification  
    D. C. Sorensen  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 2. (Apr., 1982), pp. 409-426, Jstor.  
  124. Global Convergence of a Modified Newton Iteration for Algebraic Equations  
    Kazuo Murota  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 4. (Aug., 1982), pp. 793-799, Jstor.  
  125. Convergence Acceleration for Newton's Method at Singular Points  
    D. W. Decker, C. T. Kelley  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 1. (Feb., 1982), pp. 219-229, Jstor.  
  126. Une approche combinatoire pour l'itération de Newton\mhy Raphson. (French)  
    [A combinatorial approach for Newton-Raphson iteration]
    Décoste, H.; Labelle, G.; Leroux, P.
    Adv. in Appl. Math. 3 (1982), no. 4, 407--416, Math. Sci. Net.   
  127. Newton-Raphson Extended  
    Neville W. Richards  
    The Mathematical Gazette, Vol. 65, no. 434, (Dec., 1981), pp. 294-295.  
  128. On the Convergence of Halley's Method (in Classroom Notes)  
    G. Alefeld  
    American Mathematical Monthly, Vol. 88, No. 7. (Aug. - Sep., 1981), pp. 530-536, Jstor.  
  129. On Computation of Eigenvalues for Differential Equations by Newton's Method  
    Zeev Nehari  
    Transactions of the American Mathematical Society, Vol. 263, No. 2. (Feb., 1981), pp. 397-409, Jstor.  
  130. Newton's Method for Singular Problems when the Dimension of the Null Space is > 1  
    Andreas Griewank, M. R. Osborne  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 1. (Feb., 1981), pp. 145-149, Jstor.  
  131. A Globally Convergent Ball Newton Method  
    Karl L. Nickel  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 6. (Dec., 1981), pp. 988-1003, Jstor.  
  132. A generalization of the Newton Raphson method. (Catalan)
    Gasull, Armengol
    Publ. Sec.Mat. Univ. Autònoma Barcelona No. 23 (1981), 133--138, Math. Sci. Net.   
  133. Optimal Partitioning of Newton's Method for Calculating Roots  
    Gunter Meinardus, G. D. Taylor  
    Mathematics of Computation, Vol. 35, No. 152. (Oct., 1980), pp. 1221-1230, Jstor.  
  134. Newton's Method at Singular Points. II  
    D. W. Decker, C. T. Kelley  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 3. (Jun., 1980), pp. 465-471, Jstor.  
  135. Newton's Method at Singular Points. I  
    D. W. Decker, C. T. Kelley  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 1. (Feb., 1980), pp. 66-70, Jstor.  
  136. Parameter Selection for Newton-Like Methods Applicable to Nonlinear Partial Differential Equations  
    R. E. Bank, D. J. Rose  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 6. (Dec., 1980), pp. 806-822, Jstor.  
  137. Be Careful When You Dodge Round Newton  
    F. M. Arscott  
    The Mathematical Gazette, Vol. 63, no. 425, (Oct., 1979), pp. 169-172.  
  138. Inverse Iteration, Ill-Conditioned Equations and Newton's Method  
    G. Peters, J. H. Wilkinson  
    SIAM Review, Vol. 21, No. 3. (Jul., 1979), pp. 339-360, Jstor.  
  139. A Modified Newton's Method for Unconstrained Minimization  
    Shmuel Kaniel, Achiya Dax  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 2. (Apr., 1979), pp. 324-331, Jstor.  
  140. Affine Invariant Convergence Theorems for Newton's Method and Extensions to Related Methods  
    P. Deuflhard, G. Heindl  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 1. (Feb., 1979), pp. 1-10, Jstor.  
  141. A faster modified Newton-Raphson iteration  
    Crisfield, M. A.
    Comput. Methods Appl. Mech. Engrg. 20 (1979), no. 3, 267--278, Math. Sci. Net.   
  142. Continuous Newton-Raphson method for solving an underdetermined system of nonlinear equations  
    Tanabe, Kunio
    Nonlinear Anal. 3 (1979), no. 4, 495--503, Math. Sci. Net.   
  143. On Newton's Method for Singular Problems  
    G. W. Reddien  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 993-996, Jstor.  
  144. Ideas and examples for presenting the Newton-Raphson method  
    Hart, V. G.; Howard, L. N.
    Austral. Math. Soc. Gaz. 5 (1978), no. 3, 73--89, Math. Sci. Net.   
  145. On the Convergence of a Quasi-Newton Method for Sparse Nonlinear Systems  
    Binh Lam  
    Mathematics of Computation, Vol. 32, No. 142. (Apr., 1978), pp. 447-451, Jstor.  
  146. Revision of a Derivative-Free Quasi-Newton Method  
    John Greenstadt  
    Mathematics of Computation, Vol. 32, No. 141. (Jan., 1978), pp. 201-221, Jstor.  
  147. Sufficient conditions for elementary Newton-Raphson convergence  
    Speck, G. P.
    New Zealand Math. Mag. 14 (1977), no. 1, 34--36, Math. Sci. Net.   
  148. On Halley's Variation of Newton's Method (in Classroom Notes)
    George H. Brown, Jr.  
    American Mathematical Monthly, Vol. 84, No. 9. (Nov., 1977), pp. 726-728, Jstor.  
  149. A Stable Variant of the Secant Method for Solving Nonlinear Equations  
    W. B. Gragg, G. W. Stewart  
    SIAM Journal on Numerical Analysis, Vol. 13, No. 6. (Dec., 1976), pp. 889-903, Jstor.  
  150. A Note on the Convergence of Newton's Method  
    L. B. Rall  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 1. (Mar., 1974), pp. 34-36, Jstor.  
  151. Newton's Method for Optimization Problems with Equality Constraints  
    R. A. Tapia  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 5. (Oct., 1974), pp. 874-886, Jstor.  
  152. Newton's Method for Problems with Equality Constraints  
    R. A. Tapia  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 1. (Mar., 1974), pp. 174-196, Jstor.  
  153. A Globally Converging Secant Method with Applications to Boundary Value Problems  
    E. Polak  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 3. (Jun., 1974), pp. 529-537, Jstor.  
  154. Cycling in the Newton-Raphson algorithm  
    Ascher, Marcia
    Internat. J. Math. Ed. Sci. Tech. 5 (1974), no. 2, 229--235, Math. Sci. Net.   
  155. Cayford, J. K.; Fimple, W. R.; Unger, D. G.; White, S. P.
    A finite-difference Newton-Raphson solution of the two-center electronic Schrödinger equation.
    J. Computational Phys. 16 (1974), 259--270, Math. Sci. Net.   
  156. The Use of the Secant Method in Econometric Models  
    J. Phillip Cooper, Stanley Fischer  
    The Journal of Business, Vol. 46, No. 2. (Apr., 1973), pp. 274-277, Jstor.  
  157. A Quasi-Newton Method with No Derivatives  
    John Greenstadt  
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 145-166, Jstor.  
  158. A note on some properties of the Newton-Raphson's method  
    Cheng, M. C.
    Nanta Math. 5 (1972), no. 3, 10--17, Math. Sci. Net.   
  159. A note on Newton-Raphson's method. (Japanese)  
    Sakashita, Hideo; Sasaya, Fumio
    Bull. Kyoto Univ. Ed. Ser. B No. 42 (1973), 1--2, Math. Sci. Net.   
  160. The Kantorovich Theorem for Newton's Method (in Classroom Notes)  
    R. A. Tapia  
    American Mathematical Monthly, Vol. 78, No. 4. (Apr., 1971), pp. 389-392, Jstor.  
  161. Global Convergence of Newton-Gauss-Seidel Methods  
    Jorge J. More  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 325-336, Jstor.  
  162. The Simultaneous Newton Improvement of a Complete Set of Approximate Factors of a Polynomial  
    A. A. Grau  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 425-438, Jstor.  
  163. Parameter Selection for Modified Newton Methods for Function Minimization  
    D. F. Shanno  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 3. (Sep., 1970), pp. 366-372, Jstor.  
  164. Generalized Logarithmic Error and Newton's Method for the mth Root  
    David L. Phillips  
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 383-389, Jstor.  
  165. On Aitken' s d^2  Method (in Mathematical Notes)  
    Simeon Reich  
    American Mathematical Monthly, Vol. 77, No. 3. (Mar., 1970), pp. 283-284, Jstor.  
  166. Application of a Modified Newton's Iteration Method to Construct Solutions of Eigenvalue Problems of Nonlinear Partial Differential Operators  
    Y. M. Chen; P. L. Christiansen  
    SIAM Journal on Applied Mathematics, Vol. 18, No. 2. (Mar., 1970), pp. 335-345, Jstor.  
  167. Modification of a Quasi-Newton Method for Nonlinear Equations with a Sparse Jacobian  
    L. K. Schubert  
    Mathematics of Computation, Vol. 24, No. 109. (Jan., 1970), pp. 27-30, Jstor.  
  168. Modified Newton-Raphson methods for preliminary orbit determination  
    Pitkin, Edward T.; Carpenter, Gilbert C.
    Celestial Mech. 1, (1969/1970), 72--90, Math. Sci. Net.  
  169. A modification of the Newton-Raphson algorithm in the application to the identification of dynamic objects. (Polish)  
    Latarnik, Michal
    Zeszyty Nauk. Politech. Slpolhk ask. Automat. No. 16 (1970), 35--49, Math. Sci. Net.  
  170. Geometrical Aspects of Newton's Method  
    Walter Jennings  
    Mathematics Magazine, Vol. 42, No. 5. (Nov., 1969), pp. 262-266, Jstor.  
  171. Optimal Starting Approximations for Newton's Method  
    P. H. Sterbenz, C. T. Fike  
    Mathematics of Computation, Vol. 23, No. 106. (Apr., 1969), pp. 313-318, Jstor.  
  172. A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination  
    Kenneth M. Brown  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 4. (Dec., 1969), pp. 560-569, Jstor.  
  173. Jacobi and Gauss-Seidel Methods for Nonlinear Network Problems  
    T. A. Porsching  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 3. (Sep., 1969), pp. 437-449, Jstor.  
  174. On the Kantorovich Hypothesis for Newton's Method  
    J. E. Dennis, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 3. (Sep., 1969), pp. 493-507, Jstor.  
  175. The Weak Newton Method and Boundary Value Problems  
    Richard A. Tapia  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 4. (Dec., 1969), pp. 539-550, Jstor.  
  176. A Modified Newton-Raphson Iteration (in Classroom Notes)  
    Walter Jennings  
    American Mathematical Monthly, Vol. 75, No. 6. (Jun. - Jul., 1968), pp. 652-654, Jstor.  
  177. On Steffensen's Method  
    L. W. Johnson, D. R. Scholz  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 2. (Jun., 1968), pp. 296-302, Jstor.  
  178. Optimal Starting Values for the Newton-Raphson Calculation of Inverses of Certain Functions  
    D. G. Moursund, G. D. Taylor  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 1. (Mar., 1968), pp. 138-150, Jstor.  
  179. On Newton-Raphson Iteration (in Classroom Notes)  
    J. F. Traub  
    American Mathematical Monthly, Vol. 74, No. 8. (Oct., 1967), pp. 996-998, Jstor.  
  180. Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods  
    James M. Ortega, Werner C. Rheinboldt  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 2. (Jun., 1967), pp. 171-190, Jstor.  
  181. Newton's Method for Convex Operators in Partially Ordered Spaces  
    James S. Vandergraft  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 3. (Sep., 1967), pp. 406-432, Jstor.  
  182. On Newton's Method and Nonlinear Simultaneous Displacements  
    J. E. Dennis, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 1. (Mar., 1967), pp. 103-108, Jstor.  
  183. A Stationary Newton Method for Nonlinear Functional Equations  
    J. E. Dennis, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 2. (Jun., 1967), pp. 222-232, Jstor.  
  184. Note on Newton's Method  
    L. M. Weiner  
    Mathematics Magazine, Vol. 39, No. 3. (May, 1966), pp. 143-145, Jstor.  
  185. On a Discrete Version of the Newton-Raphson Method  
    Leon Wegge  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 1. (Mar., 1966), pp. 134-142, Jstor.  
  186. Nonlinear Difference Equations and Gauss-Seidel Type Iterative Methods  
    James M. Ortega, Maxine L. Rockoff  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 3. (Sep., 1966), pp. 497-513, Jstor.  
  187. On Discretization and Differentiation of Operators with Application to Newton's Method  
    James M. Ortega, Werner C. Rheinboldt  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 1. (Mar., 1966), pp. 143-156, Jstor.  
  188. Error analysis for the Newton-Raphson method
    Lancaster, P.
    Numer. Math. 9, (1966), 55--68, Math. Sci. Net.  
  189. A Newton-Raphson method for the solution of systems of equations  
    Ben-Israel, Adi
    J. Math. Anal. Appl. 15, (1966), 243--252, Math. Sci. Net.  
  190. A modified Newton-Raphson method for the solution of systems of equations  
    Ben-Israel, Adi
    Israel J. Math. 3, (1965), 94--98, Math. Sci. Net.  
  191. Convergence of the Newton-Raphson method for arbitrary polynomials  
    Lancaster, P.
    Math. Gaz. 48, (1964), 291--295, Math. Sci. Net.  
  192. Some Applications of the Newton-Raphson Method to Non-Linear Matrix Problems  
    P. Lancaster  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 271, No. 1346. (Jan. 22, 1963), pp. 324-331, Jstor.  
  193. Erratum: Sufficient Conditions for the Convergence of Newton's Method in Complex Banach Spaces  
    Marvin L. Stein  
    Proceedings of the American Mathematical Society, Vol. 13, No. 6. (Dec., 1962), p. 1000, Jstor.  
  194. Errata: Newton's Method for the Characteristic Value Problem Ax = lambda Bx  
    L. B. Rall  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 1. (Mar., 1962), p. 228, Jstor.  
  195. Newton's Method for the Characteristic Value Problem Ax = lambda Bx  
    L. B. Rall  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 2. (Jun., 1961), pp. 288-293, Jstor.  
  196. On the Utility of Newton's Method for Computing Complex Roots of Equations (in Technical Notes and Short Papers)  
    I. M. Longman  
    Mathematics of Computation, Vol. 14, No. 70. (Apr., 1960), pp. 187-189, Jstor.  
  197. Taylor's Theorem and Newton's Method (in Classroom Notes)  
    F. D. Parker  
    American Mathematical Monthly, Vol. 66, No. 1. (Jan., 1959), p. 51, Jstor.  
  198. A modified Newton-Raphson process for approximation of multiple roots of polynomials  
    Milnes, Harold Willis  
    Indust. Math. 9, (1958), no. 2, 17--26, Math. Sci. Net.  
  199. Newton's Method and Multiple Roots  
    Thomas E. Mott  
    American Mathematical Monthly, Vol. 64, No. 9. (Nov., 1957), pp. 635-638, Jstor.  
  200. Newton's Method for Trigonometry Students (in Classroom Notes)  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 63, No. 10. (Dec., 1956), p. 722, Jstor.  
  201. Amélioration du procédé de division numérique utilisant l'itération de Newton-Raphson. (French)
    Storrer, F.
    Acad. Roy. Belg. Bull. Cl. Sci. (5) 42 (1956), 30--33, Math. Sci. Net.  
  202. Newton's Method in Banach Spaces  
    Robert G. Bartle  
    Proceedings of the American Mathematical Society, Vol. 6, No. 5. (Oct., 1955), pp. 827-831, Jstor.  
  203. Sufficient Conditions for the Convergence of Newton's Method in Complex Banach Spaces  
    Marvin L. Stein  
    Proceedings of the American Mathematical Society, Vol. 3, No. 6. (Dec., 1952), pp. 858-863, Jstor.  
  204. Another Variation of Newton's Method (in Classroom Notes)  
    J. K. Stewart  
    American Mathematical Monthly, Vol. 58, No. 5. (May, 1951), pp. 331-334, Jstor.  
  205. A Type of Variation on Newton's Method  
    H. J. Hamilton  
    American Mathematical Monthly, Vol. 57, No. 8. (Oct., 1950), pp. 517-522, Jstor.  
  206. Notes on the Graeffe Method of Root Squaring (in Mathematical Notes)  
    G. C. Best  
    American Mathematical Monthly, Vol. 56, No. 2. (Feb., 1949), pp. 91-94, Jstor.  
  207. A Modification of Newton's Method (in Classroom Notes)  
    H. S. Wall  
    American Mathematical Monthly, Vol. 55, No. 2. (Feb., 1948), pp. 90-94, Jstor.  
  208. On the Newton-Raphson method of approximation  
    Richmond, H. W.  
    Edinburgh Math. Notes 1944 (1944). no. 34, 5--8, Math. Sci. Net.  
  209. New Criteria for Accuracy in Approximating Real Roots by the Newton-Raphson Method  
    Myron G. Pawley  
    National Mathematics Magazine, Vol. 15, No. 3. (Dec., 1940), pp. 111-120, Jstor.  
  210. On the Graeffe Method of Solution of Equations  
    L. L. Cronvich  
    American Mathematical Monthly, Vol. 46, No. 4. (Apr., 1939), pp. 185-190. Jstor.  
  211. Haley's Methods for Solving Equations  
    Harry Bateman  
    American Mathematical Monthly, Vol. 45, No. 1. (Jan., 1938), pp. 11-17, Jstor.  
  212. On the Convergence of Newton's Method of Approximation (in Questions, Discussions, and Notes)  
    G. T. Coate  
    American Mathematical Monthly, Vol. 44, No. 7. (Aug. - Sep., 1937), pp. 464-466, Jstor.  
  213. Graeffe's Method and Complex Roots (in Questions, Discussions, and Notes)  
    B. A. Hausmann  
    American Mathematical Monthly, Vol. 43, No. 4. (Apr., 1936), pp. 225-229. Jstor.  
  214. On Graeffe's Method for the Numerical Solution of Algebraic Equations  
    C. A. Hutchinson  
    American Mathematical Monthly, Vol. 42, No. 3. (Mar., 1935), pp. 149-161, Jstor.  
  215. On Newton's Method of Approximation  
    Henry B. Fine  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 2, No. 9. (Sep. 15, 1916), pp. 546-552, Jstor.  
  216. Newton's Method in General Analysis  
    Albert A. Bennett  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 2, No. 10. (Oct. 15, 1916), pp. 592-598, Jstor.  
  217. Historical Note on the Newton-Raphson Method of Approximation  
    Florian Cajori  
    American Mathematical Monthly, Vol. 18, No. 2. (Feb., 1911), pp. 29-32, Jstor.  
  218. On Newton's Method of Approximation (in Notes)  
    F. Franklin  
    American Journal of Mathematics, Vol. 4, No. 1/4. (1881), pp. 275-276, Jstor.  
  219. On Sir Isaac Newton's Method of Finding the Limits of the Roots of Equations. [Abstract]  
    Herbert Panmure Ribton  
    Abstracts of the Papers Communicated to the Royal Society of London, Vol. 5. (1843 - 1850), p. 630, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004