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A Residual Existence Theorem for Linear Equations

SYSNO ASEP	0332762
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	A Residual Existence Theorem for Linear Equations
Title	Reziduální existenční věta pro soustavy lineárních rovnic
Author(s)	Rohn, Jiří (UIVT-O)_{SAI, RID, ORCID}
Source Title	Optimization Letters. - : Springer - ISSN 1862-4472 Roč. 4, č. 2 (2010), s. 287-292
Number of pages	4 s.
Language	eng - English
Country	DE - Germany
Keywords	linear equations ; solution ; existence ; residual ; convex hull ; absolute value equation
Subject RIV	BA - General Mathematics
R&D Projects	GA201/09/1957 GA ČR - Czech Science Foundation (CSF)
	GC201/08/J020 GA ČR - Czech Science Foundation (CSF)
CEZ	AV0Z10300504 - UIVT-O (2005-2011)
UT WOS	000276366600010
EID SCOPUS	77955088699
DOI	10.1007/s11590-009-0160-7
Annotation	A residual existence theorem for linear equations is proved: if $A\in\Rmn$, $b\in\Rm$ and if $X$ is a finite subset of $\Rn$ satisfying $\max_{x\in X}p^T(Ax-b)\geq 0$ for each $p\in\Rm$, then the system of linear equations $Ax=b$ has a solution in the convex hull of $X$. An application of this result to unique solvability of the absolute value equation $Ax+B\|x\|=b$ is given.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2010

Number of the records: 1