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Application of Matrix Decompositions for Matrix Canonization

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 2019 Russian Federation English Publisher:Pleiades Publishing LtdJournal:Computational Mathematics and Mathematical Physics, volume 59, pages 1,759-1,770 (issn: 0965-5425, eissn: 1555-6662,

Authors: Volkov V.; Dem’yanov D.;

doi: 10.1134/s0965542519110149

Application of Matrix Decompositions for Matrix Canonization

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Abstract

© 2019, Pleiades Publishing, Ltd. Abstract: The problem of solving overdetermined, underdetermined, singular, or ill conditioned SLAEs using matrix canonization is considered. A modification of an existing canonization algorithm based on matrix decomposition is proposed. Formulas using LU decomposition, QR decomposition, LQ decomposition, or singular value decomposition, depending on the properties of the given matrix, are obtained. A method for evaluating the condition number of the canonization problem is proposed. It is based on computing the norm of the matrices obtained as a result of canonization; this method does not require the original matrix to be inverted. A general step-by-step matrix canonization algorithm is described and implemented in MATLAB. The implementation is tested on a set of 100 000 randomly generated matrices. The testing results confirmed the validity and efficiency of the proposed algorithm.

Country

Russian Federation

Related Organizations

Kazan Federal University
Russian Federation

Keywords

LU decomposition, system of linear algebraic equations, column space, singular value decomposition, nullspace, 510, row space, QR decomposition, tablet method, LQ decomposition, matrix canonization, condition number

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