An overview of polynomially computable characteristics of special interval matrices
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10419312" target="_blank" >RIV/00216208:11320/20:10419312 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1007/978-3-030-31041-7_16" target="_blank" >https://doi.org/10.1007/978-3-030-31041-7_16</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-31041-7_16" target="_blank" >10.1007/978-3-030-31041-7_16</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
An overview of polynomially computable characteristics of special interval matrices
Popis výsledku v původním jazyce
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying polynomially solvable classes thus belongs to important current trends. The purpose of this paper is to review some of such classes. In particular, we focus on several special interval matrices and investigate their convenient properties. We consider tridiagonal matrices, M, H, P, Bmatrices, inverse M-matrices, inverse nonnegative matrices, nonnegative matrices, totally positive matrices and some others. We focus in particular on computing the range of the determinant, eigenvalues, singular values, and selected norms. Whenever possible, we state also formulae for determining the inverse matrix and the hull of the solution set of an interval system of linear equations. We survey not only the known facts, but we present some new views as well.
Název v anglickém jazyce
An overview of polynomially computable characteristics of special interval matrices
Popis výsledku anglicky
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying polynomially solvable classes thus belongs to important current trends. The purpose of this paper is to review some of such classes. In particular, we focus on several special interval matrices and investigate their convenient properties. We consider tridiagonal matrices, M, H, P, Bmatrices, inverse M-matrices, inverse nonnegative matrices, nonnegative matrices, totally positive matrices and some others. We focus in particular on computing the range of the determinant, eigenvalues, singular values, and selected norms. Whenever possible, we state also formulae for determining the inverse matrix and the hull of the solution set of an interval system of linear equations. We survey not only the known facts, but we present some new views as well.
Klasifikace
Druh
C - Kapitola v odborné knize
CEP obor
—
OECD FORD obor
50201 - Economic Theory
Návaznosti výsledku
Projekt
<a href="/cs/project/GA18-04735S" target="_blank" >GA18-04735S: Nové přístupy pro relaxační a aproximační techniky v deterministické globální optimalizaci</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název knihy nebo sborníku
Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications
ISBN
978-3-030-31041-7
Počet stran výsledku
16
Strana od-do
295-310
Počet stran knihy
649
Název nakladatele
Springer
Místo vydání
Cham
Kód UT WoS kapitoly
—