Volume no :7, Issue no: 2, February (2011)

Journal of Mathematical Sciences: Advances and Applications

NEW NUMERICAL METHOD FOR DETERMINING INERTIA AND STABILITY OF NONSYMMETRIC LARGE SPARSE MATRIX

Author's: H. Saberi Najafi and A. H. Refahi Sheikhani
Pages: [105] - [114]
Received Date: February 19, 2011
Submitted by:

Abstract

In this paper, we present a numerically stable method for determining the exact inertia of a non-symmetric large sparse matrices without computing eigenvalues. For doing this scheme, at first, we reduce a non-symmetric matrix to a symmetric tridiagonal form in a finite number of steps with a new algorithm based on the Krylov subspace method. Then, we compute the exact inertia by using an algorithm based on floating point arithmetic. Numerical tests report the effectiveness of these methods.

Keywords

Lanczos, exact inertia, non-symmetric, tridiagonal form.