About: A Residual Existence Theorem for Linear Equations

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	A Residual Existence Theorem for Linear Equations A Residual Existence Theorem for Linear Equations (en)
skos:prefLabel	A Residual Existence Theorem for Linear Equations A Residual Existence Theorem for Linear Equations (en)
skos:notation	RIV/67985807:_____/10:00332762!RIV10-AV0-67985807
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/09/1957), P(GC201/08/J020), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Rohn, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	244918
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/10:00332762
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	linear equations; solution; existence; residual; convex hull; absolute value equation (en)
http://linked.open.../riv/klicoveSlovo	absolute value equation convex hull residual linear equations existence solution
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[19807E679E9F]
http://linked.open...i/riv/nazevZdroje	Optimization Letters
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Development of methods for solving large scale nonlinear programming and nonsmooth optimization problems Verification of Hybrid Systems - Exploiting the Synergy with Underlying Constraint Solving Technology
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	4
http://linked.open...iv/tvurceVysledku	Rohn, Jiří
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	1862-4472
number of pages	4 (xsd:int)

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