An overview of polynomially computable characteristics of special interval matrices

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
An overview of polynomially computable characteristics of special interval matrices
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/GA18-04735S" target="_blank" >GA18-04735S: Novel approaches for relaxation and approximation techniques in deterministic global optimization</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Book/collection name
Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications
ISBN
978-3-030-31041-7
Number of pages of the result
16
Pages from-to
295-310
Number of pages of the book
649
Publisher name
Springer
Place of publication
Cham
UT code for WoS chapter
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