Bibliography for Broyden's Method

unabridged

 

  1. Inexact overlapped block Broyden methods for solving nonlinear equations
    Chen, Yurong; Cai, Dayong  
    Applied Mathematics and Computation (New York), v 136, n 2-3, Mar 15, 2003, p 215-228, Compendex.
  2. A Class of Revised Broyden Algorithms
    Pu, D.; Tian, W.
    Journal of Systems Science and Complexity, 2003, vol. 16, no. 2, pp. 213-221, Ingenta.
  3. Superlinear Convergence of the Sheng-Zou-Broyden Method for Nonlinear Least Squares Problems
    Ogasawara, H.; Yabe, H.
    Journal- Operations Research Society of Japan, 2003, vol. 46, no. 1, pp. 1-21, Ingenta.
  4. A Modified Broyden Method for Solving Nonconvex Minimization Problems
    Chen, Zhong  
    Wuhan Ligong Daxue Xuebao/Journal of Wuhan University of Technology, 2003, vol. 27, no. 2, pp. 191-193, Ingenta.
  5. Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch
    Xu, D.-c.
    Acta Mathematicae Applicatae Sinica English Series, 2003, vol. 19, no. 1, pp. 19-24, Ingenta.
  6. The Successive Approximation Broyden-like Algorithm for Nonlinear Complementarity Problems
    Ma, C.-f.; Liang, G.-p.
    Chinese Quarterly Journal of Mathematics, 2003, vol. 18, no. 2, pp. 146-153, Ingenta.
  7. Global convergence of Broyden's method for equality constrained optimization problems. (Chinese)  
    Jiang, Yue Ping; Wang, Fei
    Hunan Daxue Xuebao  30  (2003),  no. 3, 8--10, MathSciNet.  
  8. A Broyden numerical Kutta condition for an unsteady panel method
    Liu, P.; Bose, N.; Colbourne, B.
    International Shipbuilding Progress, 2002, vol. 49, no. DEC, pp. 263-274, Ingenta.
  9. On the convergent condition of the Broyden method
    Huang, Z.-d.
    Journal- Zhejiang University, 2002, vol. 29, no. 1, pp. 25-30, Ingenta.
  10. Globally Convergent Broyden-Like Methods for Semismooth Equations and Applications to VIP, NCP and MCP
    Li, D.-H.; Fukushima, M.
    Annals of Operations Research, 2001, vol. 103, no. 1/4, pp. 71-98, Ingenta.
  11. A nonmonotone Broyden method for unconstrained optimization.
    Liu, Guanghui; Han, Lixing; Jing, Lili
    Optim. Methods Softw. 15 (2001), no. 2, 153--171, MathSciNet.  
  12. A Note on Broyden's Method
    Ping, Z.
    Journal- China Agricultural University, 2001, vol. 6, no. 2, pp. 21-23, Ingenta.
  13. [Graphics:../Images/BroydenMethodBib_gr_1.gif]-accelerated Broyden scheme. (Chinese)    
    Lei, Fei Yan; Xing, Zhi Dong    
    Pure Appl. Math. 17 (2001), no. 2, 165--168, MathSciNet.  
  14. Derivative-free line search and global convergence of Broyden-like method for nonlinear equations
    Li, Dong-hui; Fukushima, Masao  
    Optimization Methods and Software, v 13, n 3, 2000, p 181-201, Compendex.
  15. On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating   
    Burke, J. V.; Qian, Maijian
    Math. Program.  88  (2000),  no. 1, Ser. A, 157--181, MathSciNet.  
  16. On the discovery of the "good Broyden" method.
    Broyden, C. G.
    Mathematical Programming, 2000, vol. 87, no. 2, pp. 209-213, Ingenta.
  17. Computational experiments with scaled initial Hessian approximation for the Broyden family methods.
    Al-Baali, M.; Conforti, D.; Musmanno, R.
    Optimization 48 (2000), no. 3, 375--389, MathSciNet.  
  18. A family of scaled factorized Broyden-like methods for nonlinear least squares problems.
    Zhang, J. Z.; Chen, L. H.; Deng, N. Y.
    SIAM J. Optim. 10 (2000), no. 4, 1163--1179 (electronic), MathSciNet.  
  19. Broyden's method for solving variational inequalities with global and superlinear convergence.
    Yang, Yu-fei; Li, Dong-hui
    J. Comput. Math. 18 (2000), no. 3, 289--304, MathSciNet.  
  20. On the local super-linear convergence of a matrix secant implementation of the variable metric proximal point algorithm for monotone operators   
    Qian, Maijian; Burke, James V.
    Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods (Lausanne, 1997),  317--334, Appl. Optim., 22, Kluwer Acad. Publ., Dordrecht, 1999, MathSciNet.  
  21. Acceleration of self-consistent electronic-structure calculations: Storage-saving and multiple-secant implementation of the Broyden method
    Sawamura, Akitaka; Kohyama, Masanori; Keishi, Tomohiro; Kaji, Mikio  
    Materials Transactions, JIM, v 40, n 11, Nov, 1999, p 1186-1192, Compendex.
  22. Note on a paper of Broyden.
    Roos, C.; Terlaky, T.
    Operations Research Letters, 1999, vol. 25, no. 4, pp. 183, Ingenta.
  23. Broyden's method as an ABS algorithm.
    Adib, M.; Mahdavi-Amiri, N.; Spedicato, E.
    Publ. Univ. Miskolc Ser. D Nat. Sci. Math. 40 (1999), 3--13, MathSciNet.  
  24. Adapting Broyden method to handle linear constraints imposed via Lagrange multipliers.
    Rodríguez-Ferran, Antonio; Huerta, Antonio
    Internat. J. Numer. Methods Engrg. 46 (1999), no. 12, 2011--2026, MathSciNet.  
  25. On Broyden's Method for the Regularization of Nonlinear Ill-Posed Problems.
    Kaltenbacher, B.
    Numerical functional analysis and optimization, 1998, vol. 19, no. 7/8, pp. 807-833, Ingenta.
  26. Note on a paper of C. G. Broyden: "A simple algebraic proof of Farkas's lemma and related theorems"
    Roos, Cornelis; Terlaky, Tamás
    [Optim. Methods Softw. 8 (1998), no. 3--4, 185--199; MR 99a:90181]. Oper. Res. Lett. 25 (1999), no. 4, 183--186, MathSciNet.  
  27. The convergence of Broyden's method under a weak condition. (Chinese)
    Huang, Zheng Da; Hong, Bo
    J. Hangzhou Univ. Natur. Sci. Ed. 25 (1998), no. 3, 6--11, MathSciNet.  
  28. Inexact Block Jacobi-Broyden Method for Solving Nonlinear Systems of Equations
    Yang, G.; Dutto, L. C.; Fortin, M.  
    SIAM Journal on Scientific Computing, v 18, n 5, 1997, p 1367-1392, Compendex.
  29. Alternate Broyden's method for solving linear least squares problem with multiple right-hand sides.
    Gu, Guiding
    J. Shanghai Univ. 1 (1997), no. 3, 196--201, MathSciNet.  
  30. A generalized block Broyden method for solving overdetermined systems of equations. (Chinese)
    Gu, Gui-ding
    Math. Numer. Sin. 19 (1997), no. 4, 375--384, MathSciNet.  
  31. Improved steady-state method applying Broyden's technique to the shooting method
    Ekambaram, Uma; Saleh, R.A.  
    Midwest Symposium on Circuits and Systems, v 3, 1996, p 1023-1026, Compendex.
  32. Numerical comparison of multistep quasi-Newton ABS methods with the multistep Broyden method for solving systems of nonlinear equations.
    Jeney, András
    Publ. Univ. Miskolc Ser. D Nat. Sci. Math. 36 (1996), no. 2, 47--54, MathSciNet.  
  33. An Optimal Broyden Updating Formula and its Application to Nonlinear Least Squares.
    Xu, C.-X.; Ma, X.-F.
    Optimization, 1995, vol. 35, no. 2, pp. 131, Ingenta.
  34. Why Broyden's Nonsymmetric Method Terminates on Linear Equations.
    O'Leary, Dianne P.
    SIAM journal on optimization, 1995, vol. 5, no. 2, pp. 231-235, Ingenta.
  35. Global convergence of the nonsingular Broyden method for solving unconstrained optimization problems. (Chinese)
    Li, Dong Hui
    Math. Numer. Sinica 17 (1995), no. 3, 321--330; translation in Chinese J. Numer. Math. Appl. 17 (1995), no. 4, 85--94, MathSciNet.  
  36. Broyden quasi-Newton method applied to electrical impedance tomography
    Artola, J.; Dell, J.  
    Electronics Letters, v 30, n 1, Jan 6, 1994, p 27-28, Compendex.
  37. On the affine invariant convergence theorems of inexact Newton method and Broyden's method (Chinese)
    Bai, Zhongzhi; Tong, Peili  
    Dianzi Keji Daxue Xuebao/Journal of University of Electronic Science and Technology of China, v 23, n 5, Oct, 1994, p 540, English, Compendex.
  38. A Class of Modified Broyden Algorithms.
    Ding-guo, Pu; Wei-wen, Tian
    Journal of computational mathematics, 1994, vol. 12, no. 4, pp. 366, Ingenta.
  39. Affine invariant convergence of the inexact Newton method and Broyden's method. (Chinese)
    Bai, Zhong Zhi; Tong, Pei Li
    Dianzi Keji Daxue Xuebao 23 (1994), no. 5, 535--540, MathSciNet.  
  40. Two properties of Broyden's quasi-Newton method. (Chinese)
    Meng, Ling He; Sui, Qing Mei; Shi, Zhen Jun
    Qufu Shifan Daxue Xuebao Ziran Kexue Ban 20 (1994), suppl., 82, 91, 100, 104, MathSciNet.  
  41. Sizing and Least-Change Secant Methods  
    J. E. Dennis, Jr.; H. Wolkowicz  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1291-1314, Jstor.  
  42. A Modified Broyden Update with Interpolation.
    Anjos, Miguel F.
    SIAM journal on scientific computing, 1993, vol. 14, no. 6, pp. 1359, Ingenta.
  43. Pointwise Broyden methods.
    Kelley, C. T.; Sachs, E. W.
    SIAM J. Optim. 3 (1993), no. 2, 423--441, MathSciNet.  
  44. A further discussion on convergence of the Broyden method. (Chinese)
    Wang, De Ren; Zhao, Feng Guang
    Chinese Ann. Math. Ser. A 14 (1993), no. 3, 341--349, MathSciNet.  
  45. Parallel implementations of Broyden's method
    Gomes, F.A.M.; Martinez, J.M.  
    Computing (Vienna/New York), v 47, n 3-4, 1992, p 361-366, Compendex.
  46. Nonlinear discrete-time observers using Newton's and broyden's method
    Moraal, P.E.; Grizzle, J.W.  
    Proceedings of the American Control Conference, v 4, 1992, p 3086-3090, Compendex.
  47. On the Behavior of Broyden's Class of Quasi-Newton Methods.
    Byrd, Richard H.; Liu, Dong C.; Nocedal, Jorge
    SIAM journal on optimization, 1992, vol. 2, no. 4, pp. 533-557, Ingenta.
  48. Local and Q-superlinear convergence of a class of collinear scaling algorithms that extends quasi-Newton methods with Broyden's bounded-phi class of updates.
    Ariyawansa, K. A.; Lau, D. T. M.
    Optimization 23 (1992), no. 4, 323--339, MathSciNet.                    
  49. Convergence of Broyden's method in Banach spaces.
    Hwang, D. M.; Kelley, C. T.
    SIAM J. Optim. 2 (1992), no. 3, 505--532, MathSciNet.  
  50. A faster Broyden method.    
    Kvaalen, Eric    
    BIT 31 (1991), no. 2, 369--372, MathSciNet.  
  51. On a general convergence for Broyden like update method.
    Sen, Rabindranath; Chattopadhyay, Rini; Saha, Tripti
    Internat. J. Math. Math. Sci. 14 (1991), no. 2, 349--361, MathSciNet.  
  52. A new proof of superlinear convergence for Broyden's method in Hilbert space.
    Kelley, C. T.; Sachs, E. W.
    SIAM J. Optim. 1 (1991), no. 1, 146--150, MathSciNet.
  53. A Family of Quasi-Newton Methods for Nonlinear Equations with Direct Secant Updates of Matrix Factorizations  
    Jose Mario Martinez  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 4. (Aug., 1990), pp. 1034-1049, Jstor.  
  54. Least-Change Secant Updates of Nonsquare Matrices  
    Samih K. Bourji; Homer F. Walker  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 5. (Oct., 1990), pp. 1263-1294, Jstor.  
  55. On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms.    
    Chen, X.    
    Ann. Inst. Statist. Math. 42 (1990), no. 2, 387--401, MathSciNet.  
  56. On the Gauss-Broyden method for nonlinear least squares.
    Griewank, Andreas; Sheng, Laihua
    Mathematics for large scale computing, 1--33, Lecture Notes in Pure and Appl. Math., 120, Dekker, New York, 1989, MathSciNet.
  57. A method of relaxation curve fitting in the magnetic field produced by the lung---an algorithm of the Powell symmetric Broyden update for solving the nonlinear least-square problem. (Chinese)
    Liu, Qin Sheng
    J. Numer. Methods Comput. Appl. 10 (1989), no. 3, 129--134, MathSciNet.
  58. Optimal Conditioning and Convergence in Rank One Quasi-Newton Updates  
    Chi Ming IP; Michael J. Todd  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 1. (Feb., 1988), pp. 206-221, Jstor.  
  59. Quasi-Newton Algorithms with Updates from the Preconvex Part of Broyden's Family.
    Zhang, Y.; Tewarson, R. P.
    IMA journal of numerical analysis, 1988, vol. 8, no. 4, pp. 487, Ingenta.
  60. On the development of an algorithm for solving stiff nonlinear dynamic equations based on the Broyden's updating method.
    Yuh, J.; Holley, W. E.
    Comm. Appl. Numer. Methods 4 (1988), no. 4, 483--489, MathSciNet.
  61. The Local Convergence of Broyden-Like Methods on Lipschitzian Problems in Hilbert Spaces  
    Andreas Griewank  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 3. (Jun., 1987), pp. 684-705, Jstor.  
  62. The "global" convergence of Broyden-like methods with a suitable line search.
    Griewank, Andreas
    J. Austral. Math. Soc. Ser. B 28 (1986), no. 1, 75--92, MathSciNet.
  63. Broyden's method in Hilbert space.
    Sachs, Ekkehard W.
    Math. Programming 35 (1986), no. 1, 71--82, MathSciNet.
  64. Broyden's method for a class of problems having singular Jacobian at the root  
    Decker, D. W.; Kelley, C. T.  
    SIAM J. Numer. Anal. 22 (1985), no. 3, 566--574, Jstor.  
  65. On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions  
    A. Griewank  
    SIAM Review, Vol. 27, No. 4. (Dec., 1985), pp. 537-563, Jstor.  
  66. The solution of boundary value problems by Broyden based secant methods.    
    Griewank, Andreas    
    Computational techniques and applications: CTAC-85 (Melbourne, 1985), 309--321, North-Holland, Amsterdam, 1986, MathSciNet.  
  67. Broyden's method for approximate solution of nonlinear integral equations.
    Kelley, C. T.; Sachs, E. W.
    J. Integral Equations 9 (1985), no. 1, 25--43, MathSciNet.  
  68. The convergence of matrices generated by rank-2 methods from the restricted beta-class of Broyden.
    Stoer, Josef
    Numer. Math. 44 (1984), no. 1, 37--52, MathSciNet.  
  69. Konvergenz eines angepaßten Broyden-Verfahrens zur Lösung spezieller nichtlinearer Gleichungssysteme mit schwach besetzter Jacobi-Matrix. (German)
    Mönch, Wolfgang
    [Convergence of an adapted Broyden method for the solution of special nonlinear systems of equations with sparse Jacobi matrix]
    Beiträge Numer. Math. No. 11 (1983), 93--101, MathSciNet.  
  70. Two methods of Broyden. (Portuguese)
    Martínez, J. M.; Ochi, L. S.
    Mat. Apl. Comput. 1 (1982), no. 2, 135--141, MathSciNet.  
  71. A Generalized Broyden's Method for Solving Simultaneous Linear Equations   
    Richard R. Gerber, Franklin T. Luk   
    SIAM Journal on Numerical Analysis, Vol. 18, No. 5. (Oct., 1981), pp. 882-890, Jstor.  
  72. Degenerate values for Broyden methods.
    Fletcher, R.; Sinclair, J. W.
    J. Optim. Theory Appl. 33 (1981), no. 3, 311--324, MathSciNet.  
  73. Superlinear convergence of Broyden's bounded theta -class of methods.
    Stachurski, Andrzej
    Math. Programming 20 (1981), no. 2, 196--212, MathSciNet.  
  74. Combination of the sequential secant method and Broyden's method with projected updates.
    Martínez, J. M.; Lopes, T. L.
    Computing 25 (1980), no. 4, 379--386, MathSciNet.  
  75. Some Convergence Properties of Broyden's Method   
    David M. Gay   
    SIAM Journal on Numerical Analysis, Vol. 16, No. 4. (Aug., 1979), pp. 623-630, Jstor.  
  76. Convergence Results for Schubert's Method for Solving Sparse Nonlinear Equations  
    Earl Marwil
    SIAM Journal on Numerical Analysis, Vol. 16, No. 4. (Aug., 1979), pp. 588-604, Jstor.  
  77. On the order of convergence of Broyden-Gay-Schnabel's method.    
    Martínez, J. M.    
    Comment. Math. Univ. Carolinae 19 (1978), no. 1, 107--118, MathSciNet.  
  78. Quasi-Newton Methods, Motivation and Theory  
    J. E. Dennis, Jr.; Jorge J. More  
    SIAM Review, Vol. 19, No. 1. (Jan., 1977), pp. 46-89, Jstor.  
  79. Solving systems of nonlinear equations by Broyden's method with projected updates.
    Gay, David M.; Schnabel, Robert B.
    Nonlinear programming, 3 (Proc. Sympos., Special Interest Group Math. Programming, Univ. Wisconsin, Madison, Wis., 1977), pp. 245--281, Academic Press, New York-London, 1978, MathSciNet.  
  80. On the Global Convergence of Broyden's Method   
    J. J. More, J. A. Trangenstein   
    Mathematics of Computation, Vol. 30, No. 135. (Jul., 1976), pp. 523-540, Jstor.  
  81. On the Convergence of Broyden's Method for Nonlinear Systems of Equations   
    J. E. Dennis, Jr.   
    Mathematics of Computation, Vol. 25, No. 115. (Jul., 1971), pp. 559-567, Jstor.  
  82. On some methods based on Broyden's secant approximation to the Hessian.    
    Dennis, J. E., Jr.    
    Numerical methods for non-linear optimization (Conf., Dundee, 1971), pp. 19--34. Academic Press, London, 1972, MathSciNet.  
  83. 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.  
  84. Interpolative Solution of Systems of Nonlinear Equations  
    Stephen M. Robinson  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 4. (Dec., 1966), pp. 650-658, Jstor.  
  85. A Class of Methods for Solving Nonlinear Simultaneous Equations  
    C. G. Broyden  
    Mathematics of Computation, Vol. 19, No. 92. (Oct., 1965), pp. 577-593, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005