Bibliography for Broyden's Method

short

  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 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.
  3. 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.
  4. 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.  
  5. On the discovery of the "good Broyden" method.
    Broyden, C. G.
    Mathematical Programming, 2000, vol. 87, no. 2, pp. 209-213, Ingenta.
  6. 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.  
  7. 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.
  8. 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.  
  9. 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.
  10. 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.
  11. 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.  
  12. 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.
  13. A Class of Modified Broyden Algorithms.
    Ding-guo, Pu; Wei-wen, Tian
    Journal of computational mathematics, 1994, vol. 12, no. 4, pp. 366, Ingenta.
  14. 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.  
  15. A Modified Broyden Update with Interpolation.
    Anjos, Miguel F.
    SIAM journal on scientific computing, 1993, vol. 14, no. 6, pp. 1359, Ingenta.
  16. A faster Broyden method.    
    Kvaalen, Eric    
    BIT 31 (1991), no. 2, 369--372, MathSciNet.  
  17. 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.  
  18. 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.  
  19. 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.  
  20. 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.
  21. 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.  
  22. 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.
  23. 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.  
  24. 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.
  25. 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.  
  26. 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.  
  27. 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.  
  28. 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.  
  29. 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.  
  30. 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.  
  31. 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.  
  32. 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.  
  33. 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.  
  34. 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.  
  35. 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.  
  36. 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.  
  37. 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.  
  38. 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.  
  39. 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