Simultaneous tridiagonalisation of two symmetric matrices

SD Garvey, F Tisseur, MI Friswell, U Prells, JET Penny

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)


We show how to simultaneously reduce a pair of symmetric matrices to tridiagonal form by congruence transformations. No assumptions are made on the nonsingularity or definiteness of the two matrices. The reduction follows a strategy similar to the one used for the tridiagonalization of a single symmetric matrix via Householder reflectors. Two algorithms are proposed, one using non­orthogonal rank­one modifications of the identity matrix and the other, more costly but more stable, using a combination of Householder reflectors and non­orthogonal rank­one modifications of the identity matrix with minimal condition numbers. Each of these tridiagonalization processes requires O(n^3) arithmetic operations and respects the symmetry of the problem. We illustrate and compare the two algorithms with some numerical experiments.
Translated title of the contributionSimultaneous tridiagonalisation of two symmetric matrices
Original languageEnglish
Pages (from-to)1643 - 1660
Number of pages18
JournalInternational Journal for Numerical Methods in Engineering
Publication statusPublished - Jul 2003

Bibliographical note

Publisher: John Wiley & Sons

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