THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10159151" target="_blank" >RIV/00216208:11320/13:10159151 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1137/120884237" target="_blank" >http://dx.doi.org/10.1137/120884237</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/120884237" target="_blank" >10.1137/120884237</a>

Result language

angličtina

Original language name

THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES

Original language description

This paper focuses on total least squares (TLS) problems AX ~ B with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnetynkova et al., SIAM J. Matrix Anal. Appl., 32, 2011, pp. 748-770]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakos, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861-875] showed how necessary and sufficient information for solving Ax ~ b can be revealed from the original data throughthe so-called core problem concept. In this paper we present a theoretical study extending this concept to problems with multiple right-hand sides. The data reduction we present here is based on the singular value decomposition of the system matrix A. Weshow minimality of the reduced problem; in this sense the situation is analogous to the single right-hand side case. Some other properties of the core problem, however, cannot be extended to the case of multiple right-hand sides.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F09%2F0917" target="_blank" >GA201/09/0917: Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SIAM Journal on Matrix Analysis and Applications

ISSN

0895-4798

e-ISSN

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Volume of the periodical

34

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

15

Pages from-to

917-931

UT code for WoS article

000325092700004

EID of the result in the Scopus database

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