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  • Soustava lineárních intervalových rovnic se nazývá řešitelnou, jestliže každá soustava, kterou obsahuje, je řešitelná. V hlavním výsledku tohoto článku je dokázáno, že řešitelnost soustavy lineárních intervalových rovnic s obecnou obdélníkovou maticí lze charakterizovat v termínech nezáporné řešitelnosti konečného, avšak exponenciálního počtu soustav lineárních rovnic; je dokázáno, že problém je NP-těžký. Dále je ukázáno, že tři dříve publikované výsledky jsou důsledky hlavní věty a že analogická úloha pro soustavy lineárních intervalových nerovností je řešitelná mnohem jednodušeji. (cs)
  • A system of linear interval equations is called solvable if each system of linear equations contained therein is solvable. In the main result of this paper it is proved that solvability of a general rectangular system of linear interval equations can be characterized in terms of nonnegative solvability of a finite number of systems of linear equations which, however, is exponential in matrix sizeů the problem is proved to be NP-hard. It is shown that three earlier published results are consequences of the main theorem, which is compared with its counterpart valid for linear interval inequalities that turn out to be much less difficult to solve.
  • A system of linear interval equations is called solvable if each system of linear equations contained therein is solvable. In the main result of this paper it is proved that solvability of a general rectangular system of linear interval equations can be characterized in terms of nonnegative solvability of a finite number of systems of linear equations which, however, is exponential in matrix sizeů the problem is proved to be NP-hard. It is shown that three earlier published results are consequences of the main theorem, which is compared with its counterpart valid for linear interval inequalities that turn out to be much less difficult to solve. (en)
Title
  • Řešitelnost soustav lineárních intervalových rovnic (cs)
  • Solvability of Systems of Linear Interval Equations
  • Solvability of Systems of Linear Interval Equations (en)
skos:prefLabel
  • Řešitelnost soustav lineárních intervalových rovnic (cs)
  • Solvability of Systems of Linear Interval Equations
  • Solvability of Systems of Linear Interval Equations (en)
skos:notation
  • RIV/67985807:_____/03:00103313!RIV/2005/AV0/A06005/N
http://linked.open.../vavai/riv/strany
  • 237;245
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/01/0343), Z(AV0Z1030915)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 627702
http://linked.open...ai/riv/idVysledku
  • RIV/67985807:_____/03:00103313
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • linear interval equations; solvability; complexity; linear interval inequalities (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [B4AC918C953E]
http://linked.open...i/riv/nazevZdroje
  • SIAM Journal on Matrix Analysis and Applications
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 25
http://linked.open...iv/tvurceVysledku
  • Rohn, Jiří
http://linked.open...n/vavai/riv/zamer
issn
  • 0895-4798
number of pages
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