On sparse and symmetric matrix updating subject to a linear equation

Toint, Ph. L.

doi:10.1090/S0025-5718-1977-0455338-4

On sparse and symmetric matrix updating subject to a linear equation
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by Ph. L. Toint PDF

Math. Comp. 31 (1977), 954-961 Request permission

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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