КФУ. Карточка публикации. Application of Matrix Decompositions for Matrix Canonization

КАЗАНСКИЙ
ФЕДЕРАЛЬНЫЙ УНИВЕРСИТЕТ

RUS

- EN
- 中文
- ES

APPLICATION OF MATRIX DECOMPOSITIONS FOR MATRIX CANONIZATION

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2019

Авторы, сотрудники КФУ

Демьянов Дмитрий Николаевич, автор

Авторы, аспиранты КФУ

Волков Василий Геннадьевич, автор

Библиографическое описание на языке оригинала

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

Аннотация

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.

Ключевые слова

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

Название журнала

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS

Издательство

Pleiades Publishing

URL

https://doi.org/10.1134/S0965542519110149

Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку

https://repository.kpfu.ru/?p_id=225209

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Демьянов Дмитрий Николаевич	ru_RU
dc.contributor.author	Волков Василий Геннадьевич	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/?p_id=225209	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	Статьи в зарубежных журналах и сборниках	ru_RU