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

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