Stable Factorizations of Symmetric Tridiagonal and Triadic Matrices | Zendy

Hawren Fang | Zendy; Dianne P. O’Leary | Zendy

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Stable Factorizations of Symmetric Tridiagonal and Triadic Matrices

Author(s) -

Hawren Fang,

Dianne P. O’Leary

Publication year - 2006

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/050636280

Subject(s) - tridiagonal matrix , mathematics , diagonal , triangular matrix , block matrix , combinatorics , band matrix , matrix (chemical analysis) , factorization , identity matrix , symmetric matrix , diagonal matrix , matrix decomposition , main diagonal , sparse matrix , pure mathematics , square matrix , algorithm , eigenvalues and eigenvectors , geometry , physics , materials science , composite material , quantum mechanics , invertible matrix , gaussian

We call a matrix triadic if it has no more than two nonzero o-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider LXLT factorizations of symmetric triadic matrices, where L is unit lower triangular and X is diagonal, block diagonal with 1 1a nd 22 blocks, or the identity with L lower triangular. We prove that with diagonal pivoting, the LXLT factorization of a symmetric triadic matrix is sparse, study some pivoting algorithms, discuss their growth factor and performance, analyze their stability, and develop perturbation bounds. These factorizations are useful in computing inertia, in solving linear systems of equations, and in determining modied Newton search directions.

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