KFU. Card publication. Application of Matrix Decompositions for Matrix Canonization

KAZAN
FEDERAL UNIVERSITY

- RUS
- 中文
- ES

APPLICATION OF MATRIX DECOMPOSITIONS FOR MATRIX CANONIZATION

Form of presentation

Articles in international journals and collections

Year of publication

2019

Authors, employees of KFU

Demyanov Dmitriy Nikolaevich, author

Authors, postgraduates KFU

Volkov Vasiliy Gennadevich, postgraduate kfu

Bibliographic description in the original language

Volkov, V.G., Dem?yanov, D.N. Application of Matrix Decompositions for Matrix Canonization. Comput. Math. and Math. Phys. 59, 1759?1770 (2019).

Annotation

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.

Keywords

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

The name of the journal

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS

Publishing house

Pleiades Publishing

URL

https://doi.org/10.1134/S0965542519110149

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=225209&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Demyanov Dmitriy Nikolaevich	ru_RU
dc.contributor.author	Volkov Vasiliy Gennadevich	ru_RU
dc.date.accessioned	2019-01-01T00:00:00Z	ru_RU
dc.date.available	2019-01-01T00:00:00Z	ru_RU
dc.date.issued	2019	ru_RU
dc.identifier.citation	Volkov, V.G., Dem?yanov, D.N. Application of Matrix Decompositions for Matrix Canonization. Comput. Math. and Math. Phys. 59, 1759?1770 (2019).	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=225209&p_lang=2	ru_RU
dc.description.abstract	COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS	ru_RU
dc.description.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.	ru_RU
dc.language.iso	ru	ru_RU
dc.publisher	Pleiades Publishing	ru_RU
dc.subject	system of linear algebraic equations	ru_RU
dc.subject	matrix canonization	ru_RU
dc.subject	tablet method	ru_RU
dc.subject	singular value decomposition	ru_RU
dc.subject	QR decomposition	ru_RU
dc.subject	LQ decomposition	ru_RU
dc.subject	LU decomposition	ru_RU
dc.subject	condition number	ru_RU
dc.subject	nullspace	ru_RU
dc.subject	row space	ru_RU
dc.subject	column space	ru_RU
dc.title	Application of Matrix Decompositions for Matrix Canonization	ru_RU
dc.type	Articles in international journals and collections	ru_RU