On sparse and symmetric matrix updating subject to a linear equation

Author:
Ph. L. Toint

Journal:
Math. Comp. **31** (1977), 954-961

MSC:
Primary 65F30

DOI:
https://doi.org/10.1090/S0025-5718-1977-0455338-4

MathSciNet review:
0455338

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Abstract | References | Similar Articles | Additional Information

Abstract: A procedure for symmetric matrix updating subject to a linear equation and retaining any sparsity present in the original matrix is derived. The main feature of this procedure is the reduction of the problem to the solution of an *n* dimensional sparse system of linear equations. The matrix of this system is shown to be symmetric and positive definite. The method depends on the Frobenius matrix norm. Comments are made on the difficulties of extending the technique so that it uses more general norms, the main points being shown by a numerical example.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0455338-4

Keywords:
Matrix updating,
quasi-Newton methods,
unconstrained optimization

Article copyright:
© Copyright 1977
American Mathematical Society