Original scientific paper

Symmetric indefinite factorization of quasidefinite matrices

Sanja Singer
Singer Saša

Abstract

Matrices with special structures arise in numerous applications. In
some cases, such as quasidefinite matrices or their generalizations,
we can exploit this special structure. If the matrix H is quasidefinite,
we propose a new variant of the symmetric indefinite factorization.
We show that linear system Hz = b, H quasidefinite
with a special structure, can be interpreted as an equilibrium system.
So, even if some blocks in H are ill--conditioned, the important part of solution vector z can be accurately computed. In the case of a
generalized quasidefinite matrix, we derive bounds on number of its
positive and negative eigenvalues.

Keywords

quasidefinite matrices; inertia; special linear systems; accurate solution

Hrčak ID:

1733

URI

https://hrcak.srce.hr/1733

Publication date:

20.6.1999.

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