Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F30

Retrieve articles in all journals with MSC: 65F30

Additional Information

Keywords: Matrix updating, quasi-Newton methods, unconstrained optimization
Article copyright: © Copyright 1977 American Mathematical Society