This HTML5 document contains 42 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
n13http://linked.opendata.cz/resource/domain/vavai/riv/tvurce/
n10http://linked.opendata.cz/resource/domain/vavai/projekt/
n16http://linked.opendata.cz/ontology/domain/vavai/
n18http://linked.opendata.cz/resource/domain/vavai/zamer/
shttp://schema.org/
skoshttp://www.w3.org/2004/02/skos/core#
n3http://linked.opendata.cz/ontology/domain/vavai/riv/
n2http://linked.opendata.cz/resource/domain/vavai/vysledek/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
n8http://linked.opendata.cz/ontology/domain/vavai/riv/klicoveSlovo/
n4http://linked.opendata.cz/ontology/domain/vavai/riv/duvernostUdaju/
xsdhhttp://www.w3.org/2001/XMLSchema#
n11http://linked.opendata.cz/resource/domain/vavai/vysledek/RIV%2F67985807%3A_____%2F10%3A00332762%21RIV10-AV0-67985807/
n14http://linked.opendata.cz/ontology/domain/vavai/riv/jazykVysledku/
n6http://linked.opendata.cz/ontology/domain/vavai/riv/aktivita/
n12http://linked.opendata.cz/ontology/domain/vavai/riv/druhVysledku/
n9http://linked.opendata.cz/ontology/domain/vavai/riv/obor/
n15http://reference.data.gov.uk/id/gregorian-year/

Statements

Subject Item
n2:RIV%2F67985807%3A_____%2F10%3A00332762%21RIV10-AV0-67985807
rdf:type
skos:Concept n16:Vysledek
dcterms: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.
dcterms:title
A Residual Existence Theorem for Linear Equations A Residual Existence Theorem for Linear Equations
skos:prefLabel
A Residual Existence Theorem for Linear Equations A Residual Existence Theorem for Linear Equations
skos:notation
RIV/67985807:_____/10:00332762!RIV10-AV0-67985807
n3:aktivita
n6:Z n6:P
n3:aktivity
P(GA201/09/1957), P(GC201/08/J020), Z(AV0Z10300504)
n3:cisloPeriodika
2
n3:dodaniDat
n15:2010
n3:domaciTvurceVysledku
n13:9203974
n3:druhVysledku
n12:J
n3:duvernostUdaju
n4:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
244918
n3:idVysledku
RIV/67985807:_____/10:00332762
n3:jazykVysledku
n14:eng
n3:klicovaSlova
linear equations; solution; existence; residual; convex hull; absolute value equation
n3:klicoveSlovo
n8:existence n8:residual n8:convex%20hull n8:solution n8:linear%20equations n8:absolute%20value%20equation
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[19807E679E9F]
n3:nazevZdroje
Optimization Letters
n3:obor
n9:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n10:GA201%2F09%2F1957 n10:GC201%2F08%2FJ020
n3:rokUplatneniVysledku
n15:2010
n3:svazekPeriodika
4
n3:tvurceVysledku
Rohn, Jiří
n3:zamer
n18:AV0Z10300504
s:issn
1862-4472
s:numberOfPages
4