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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 0455338
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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: http://dx.doi.org/10.1090/S0025-5718-1977-0455338-4
PII: S 0025-5718(1977)0455338-4
Keywords: Matrix updating, quasi-Newton methods, unconstrained optimization
Article copyright: © Copyright 1977 American Mathematical Society