Matrix inverse-free algorithms for the general eigenvalue problem

Mohammed A Hasan, A. A. Hasan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

There are numerous applications in sciences, engineering and mathematics that give rise to problems involving the computation of orthogonal projections onto selective invariant subspaces of matrices. Conventional algorithms for subspace estimation based upon eigenvalue decomposition (EVD) or singular value decomposition (SVD) are, however, both expensive to compute, and difficult to make recursive or implement in parallel. In contrast, algorithms based on the QR factorization have established pipelinable architectures. In this paper, we introduce novel matrix-inverse free algorithms for block matrix decomposition. They involve a combination of Newton's method and the QR factorization. Some of these methods can be shown to have cubic or quadratic convergence rates, while others can be of any desirable convergent rate.

Original languageEnglish (US)
Title of host publicationISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings
Pages353-356
Number of pages4
DOIs
StatePublished - Dec 1 2001
Event2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001 - Sydney, NSW, Australia
Duration: May 6 2001May 9 2001

Publication series

NameISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings
Volume3

Other

Other2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001
CountryAustralia
CitySydney, NSW
Period5/6/015/9/01

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