The convergence of an algorithm for solving sparse nonlinear systems-Reference-Cited by-同舟云学术

The convergence of an algorithm for solving sparse nonlinear systems

Published:1971 Issue:114 Volume:25 Page:285-294
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Broyden C. G.

Abstract

A new algorithm for solving systems of nonlinear equations where the Jacobian is known to be sparse is shown to converge locally if a sufficiently good initial estimate of the solution is available and if the Jacobian satisfies a Lipschitz condition. The results of numerical experiments are quoted in which systems of up to 600 equations have been solved by the method.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1971-25-114/S0025-5718-1971-0297122-5/S0025-5718-1971-0297122-5.pdf

Reference14 articles.

1. A class of methods for solving nonlinear simultaneous equations;Broyden, C. G.;Math. Comp.,1965

2. A new method of solving nonlinear simultaneous equations;Broyden, C. G.;Comput. J.,1969

3. The convergence of single-rank quasi-Newton methods;Broyden, C. G.;Math. Comp.,1970

4. A. Chang, Applications of Sparse Matrix Methods in Electric Power Systems Analysis, Proc. Sympos. on Sparse Matrices and Their Applications (IBM Watson Research Center, 1968), RA 1 #11707, Watson Research Center, Yorktown Heights, New York, 1969.

5. The application of the method of the variation of a parameter to the construction of iteration formulae of heightened precision for the determination of numerical solutions of non-linear integral equations;Davidenko, D. F.;Dokl. Akad. Nauk SSSR,1965

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