]*>","")" /> 广义块Broyden方法与超定方程组求解

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广义块Broyden方法与超定方程组求解

顾桂定   

  1. 上海大学数学系
  • 出版日期:1997-04-14 发布日期:1997-04-14

顾桂定. 广义块Broyden方法与超定方程组求解[J]. 计算数学, 1997, 19(4): 375-384.

A GENERALIZED BLOCK BROYDEN'S METHOD FOR SOLVING OVERDETERMINED EQUATIONS

  1. Gu Gui-ding (Shanghai University, Mathematics Department, Shanghai)
  • Online:1997-04-14 Published:1997-04-14
In this paper, a generalized block Broyden's method is presented for solvinga collection of overdetermined equations. We have proven that for the p linear overdetermined equations with a m×n coefficient matrix, the method is terminated with the p least squared solutions after 2m/p steps at most, and two numerical examples are given.
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[1] Dianne P. O’Leary A.Yeremin, The linear algebra of block quasi-newton algorithms,Linear Algebra Appl, 212/213(1994), 153-168.
[2] R. R. Gerber, F. T. Luk, A generalized broyden’s method for solving simultaneous linear equations, SIAM, J. Numer, Anal, 18(1981), 882-890.
[3] D. M. Gay,Some convergence properties of broyden’s method,SIAM J.Numer. Anal, 16(1979),623-630.
[4] J. E. Dennis, Jr, R. B. Schnabel, Numerical Methods for Unconstrained Optimizstion and Nonlinear Equations, Prentice-Hall, 1983.
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