Bibliography for Brent's Method

short

  1. Modifications of the interval-Newton-method with improved asymptotic efficiency.  
    Alefeld, G. E.; Potra, F. A.; Völker, W.
    BIT  38  (1998),  no. 4, 619--635, MathSciNet.  
  2. Algorithm 835: MULTROOT - A matlab package for computing polynomial roots and multiplicities
    Zeng, Zhonggang
    ACM Transactions on Mathematical Software, v 30, n 2, June, 2004, p 218-236, Compendex  
  3. A class of discretized Newton methods for solving systems of nonlinear equations. (Chinese)  
    Chen, Zhi; Gao, Lu-duan; Deng, Nai-yang
    Math. Numer. Sin.  20  (1998),  no. 1, 57--68, MathSciNet.  
  4. New hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using derivatives
    Chandrupatla, Tirupathi R.
    Advances in Engineering Software, v 28, n 3, Apr, 1997, p 145-149, Compendex.
  5. Improved Illinois-type methods for the solution of nonlinear equations.  
    Ford, J. A.
    Sci. Iran.  4  (1997),  no. 1-2, 28--34, MathSciNet.  
  6. A note on Brent's rootfinding method.    
    Potra, F. A.; Shi, Y.    
    Numerical methods and error bounds (Oldenburg, 1995), 188--197, Math. Res., 89, Akademie Verlag, Berlin, 1996, MathSciNet.  
  7. The semilocal convergence of a generalization of Brent's and Brown's methods.    
    Huang, Zhi Jian    
    Numer. Algorithms 6 (1994), no. 1-2, 37--62, MathSciNet.  
  8. On the Convergence of the Brent Method.
    De-ren, Wang; Zhi-jian, Huang
    Journal of computational mathematics, 1994, vol. 12, no. 1, pp. 1-20, Ingenta.   
  9. Rounding errors in algebraic processes  
    Wilkinson, J. H.
    Reprint of the 1963 original [Prentice-Hall, Englewood Cliffs, NJ; MR0161456 (28 \#4661)]. Dover Publications, Inc., New York, 1994, MathSciNet.  
  10. Some efficient methods for enclosing simple zeros of nonlinear equations.  
    Alefeld, Götz E.; Potra, Florian A.
    BIT  32  (1992),  no. 2, 334--344, MathSciNet.  
  11. PRAXIS: Brent's Algorithm for Function Minimization.
    Gegenfurtner, Karl R.
    Behavior research methods, instruments, & computers, 1992, vol. 24, no. 4, pp. 560 , Ingenta.   
  12. Solver for f(x) = 0
    Grossman, Nathaniel
    Journal of Forth Application and Research, v 5, n 2, 1988, p 287-304, Compendex.
  13. On Enclosing Simple Roots of Nonlinear Equations  
    G. Alefeld; F. A. Potra; Yixun Shi  
    Mathematics of Computation, Vol. 61, No. 204. (Oct., 1993), pp. 733-744, Jstor.  
  14. A Simplified Version of the Fast Algorithms of Brent and Salamin  
    D. J. Newman  
    Mathematics of Computation, Vol. 44, No. 169. (Jan., 1985), pp. 207-210, Jstor.  
  15. A Rapid Robust Rootfinder  
    Richard I. Shrager  
    Mathematics of Computation, Vol. 44, No. 169. (Jan., 1985), pp. 151-165, Jstor.  
  16. On the global convergence of the modified Brent method. (Korean)    
    Kim, Byong Bae    
    Cho-u on In-min Kong-hwa-kuk Kwa-hak-w\u on T'ong-bo 1983, no. 1, 4--8, MathSciNet.  
  17. Zur Effektivität mehrstufiger Brown-Brent-Verfahren. (German)
    [On the efficiency of multistage Brown-Brent methods]   
    Hoyer, Wolfgang    
    Beiträge Numer. Math. No. 10 (1981), 57--69, MathSciNet.  
  18. Solving nonlinear simultaneous equations with a generalization of Brent's method.    
    Martínez, José Mario    
    BIT 20 (1980), no. 4, 501--510, MathSciNet.  
  19. Ergebnisse zum Brown-Brent-Verfahren zur numerischen Lösung nichtlinearer Gleichungssysteme. (German)
    Schmidt, Jochen W.
    Wiss. Z. Tech. Univ. Dresden 29 (1980), no. 2, 442--445, MathSciNet.  
  20. The Pegasus methods for the solution of nonlinear equations. (Hungarian)  
    Kalmár, János
    Alkalmaz. Mat. Lapok  5  (1979), no. 3-4, 277--288 (1980), MathSciNet.  
  21. Generalization of the Methods of Brent and Brown for Solving Nonlinear Simultaneous Equations   
    Jose Mario Martinez
    SIAM Journal on Numerical Analysis, Vol. 16, No. 3. (Jun., 1979), pp. 434-448, Jstor.  
  22. Personal calculator has key to solve any equation f(x)=0.  
    Kahan, William M.
    Hewlett-Packard J.  30  (1979), no. 12, 20--26, MathSciNet.  
  23. Efficient Acceleration Techniques for Fixed Point Algorithms  
    R. Saigal; M. J. Todd  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 997-1007, Jstor.  
  24. The Brown-Brent method for systems of nonlinear equations.    
    Schmidt, J. W.    
    Proceedings of the Fourth Symposium on Basic Problems of Numerical Mathematics (Plze\v n, 1978), pp. 163--171, Charles Univ., Prague, 1978, MathSciNet.  
  25. COMPARISON OF A CONTINUATION METHOD WITH BRENT'S METHOD FOR THE NUMERICAL SOLUTION OF A SINGLE NONLINEAR EQUATION.
    Swift, A.; Lindfield, G. R.
    Computer Journal, v 21, n 4, Nov, 1978, p 359-362, Compendex.
  26. Die Verfahren vom Brown-Brent-Typ bei gemischt linearen-nichtlinearen Gleichungssystemen. (German)
    Schmidt, Jochen W.; Hoyer, Wolfgang
    Z. Angew. Math. Mech. 58 (1978), no. 10, 425--428, MathSciNet.  
  27. Multiple-precision zero-finding methods and the complexity of elementary function evaluation.  
    Brent, Richard P.
    Analytic computational complexity (Proc. Sympos., Carnegie-Mellon Univ., Pittsburgh, Pa., 1975),  pp. 151--176. Academic Press, New York, 1976, MathSciNet.  
  28. Ein Konvergenzsatz für Verfahren vom Brown-Brent-Typ. (German)
    Schmidt, Jochen W.; Hoyer, Wolfgang
    Z. Angew. Math. Mech. 57 (1977), no. 7, T397--T405, MathSciNet.  
  29. Computer Methods for Mathematical Computations  
    Forsythe, G. E., M. A. Malcolm, and C. B. Moler
    Prentice-Hall, 1976.
  30. Some high-order zero-finding methods using almost orthogonal polynomials  
    R. P. Brent  
    J. Australian Mathematical Society (Series B)  19 (1975), 1-29.  
  31. A class of optimal-order zero-finding methods using derivative evaluations  
    R. P. Brent  
    Analytic Computational Complexity, Academic Press, 1975, 59-73.
  32. Multiple-precision zero-finding methods and the complexity of elementary function evaluation  
    R. P. Brent  
    Analytic Computational Complexity, Academic Press, New York, 1975, 151-176.
  33. Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function  
    J. C. P. Bus and T. J. Dekker  
    ACM Transactions of Mathematical Software, Vol. 1 No. 4 (1975) 330-345, MathSciNet.  
  34. High order search methods for finding roots.  
    Micchelli, C. A.; Miranker, W. L.
    J. Assoc. Comput. Mach.  22  (1975), 51--60, MathSciNet.  
  35. A Note on Chambers' Method  
    J. A. Blackburn; Y. Beaudoin  
    Mathematics of Computation, Vol. 28, No. 126. (Apr., 1974), pp. 573-574, Jstor.  
  36. Some efficient algorithms for solving systems of nonlinear equations  
    Richard P. Brent
    SIAM Journal on Numerical Analysis, Vol. 10, No. 2. (Apr., 1973), pp. 327-344, Jstor.  
  37. An improved Pegasus method for root finding
    King, Richard F.
    Nordisk Tidskr. Informationsbehandling (BIT)  13  (1973), 423--427., MathSciNet.  
  38. Algorithms for Minimization Without Derivatives  
    Brent, R.  
    Prentice-Hall, 1973.
  39. Optimal iterative processes for root-finding  
    Brent, Richard; Winograd, Shmuel; Wolfe, Philip  
    Numer. Math.  20  (1972/73), 327--341, MathSciNet.  
  40. An optimal secant method for solving systems of nonlinear equations  
    R. P. Brent  
    IBM Technical Disclosure Bulletin 15 (1972), 1216-1217.  
  41. On the Davidenko-Branin method for solving simultaneous nonlinear equations  
    R. P. Brent  
    IBM J. Research and Development 16 (1972), 434-436.  
  42. A Note on Chambers' Method for Finding a Zero of a Function
    M. G. Cox
    Mathematics of Computation, Vol. 26, No. 119. (Jul., 1972), pp. 749-750, Jstor.  
  43. The "Pegasus" method for computing the root of an equation
    Dowell, M.; Jarratt, P.
    Nordisk Tidskr. Informationsbehandling (BIT)  12  (1972), 503--508, MathSciNet.  
  44. An algorithm with guaranteed convergence for finding a zero of a function
    R. P. Brent
    Computer Journal, 14 (1971) 422-425.
  45. A modified Regula Falsi method for computing the root of an equation  
    Dowell, M.; Jarratt, P.
    Nordisk Tidskr. Informationsbehandling (BIT)  11  (1971), 168--174, MathSciNet.  
  46. A bracketing technique for computing a zero of a function.
    Cox, M. G.
    Comput. J. 13 1970 101--102, MathSciNet.  
  47. Eigenvalues of  A X= lambda B X  with band symmetric A and B.  
    Peters, G.; Wilkinson, J. H.
    Comput. J.  12  1969 398--404, MathSciNet.  
  48. Constructive aspects of the fundamental theorem of algebra.
    Edited by Bruno Dejon and Peter Henrici
    Proceedings of a Symposium Conducted at the IBM Research Laboratory, Zürich-Rüschlikon, June 5-7, 1967. Wiley-Interscience A Division of John Wiley & Sons, Ltd., London-New York-Sydney 1969 vii+337 pp.
  49. Finding a zero by means of successive linear interpolation
    Dekker, T. J.
    Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967),  pp. 37--48, Wiley-Interscience, 1969, New York, MathSciNet.  
  50. Remarks on the paper by Dekker
    Forsythe, George E.
    Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967), pp. 49--51, Wiley-Interscience, 1969, New York, MathSciNet.  
  51. An iterative method for locating turning points
    Jarratt, P.
    The Computer Journal, Vol. 10.,  (1967), pp. 82-4.
  52. Two algorithms based on successive linear interpolation  
    J. H. Wilkinson
    Technical Report CS 60 , (1967), Computer Science Department, Stanford University.
  53. A contribution to the development of ALGOL
    Wirth, N., and Hoare, C. A. R.
    CACM, Vol. 9, pp. 413-431.
  54. Programs AP 200 and AP 230 de serie AP 200  
    A. van Wijngaarden, J. A. Zonneveld and E. W. Dijkstra and edited by T. J. Dekker  
    The Mathematical Centre,  (1963), Amsterdam.  
  55. Rounding errors in algebraic processes  
    Wilkinson, J. H.
    Prentice-Hall, Inc., Englewood Cliffs, N.J. 1963 vi+161 pp.
  56. Solution of certain large sets of equations on Pegasus using matrix methods  
    Wilson, L. B.
    Comput. J.  2  1959 130--133.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005