Determinants of interval matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385604" target="_blank" >RIV/00216208:11320/18:10385604 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=hf9xeTVo09" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=hf9xeTVo09</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.13001/1081-3810.3719" target="_blank" >10.13001/1081-3810.3719</a>
Alternative languages
Result language
angličtina
Original language name
Determinants of interval matrices
Original language description
In this paper we shed more light on determinants of real interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the state-of-the-art method, however, it is less consuming regarding computational time. Other methods transferable from real matrices (e.g., the Gerschgorin circles, Hadamard's inequality) are discussed. New results about classes of interval matrices with polynomially computable tasks related to determinant are proved (symmetric positive definite matrices, class of matrices with identity midpoint matrix, tridiagonal H-matrices). The mentioned methods were compared for random general and symmetric matrices.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
50201 - Economic Theory
Result continuities
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)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal Of Linear Algebra
ISSN
1537-9582
e-ISSN
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Volume of the periodical
33
Issue of the periodical within the volume
November
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
99-112
UT code for WoS article
000485374300010
EID of the result in the Scopus database
2-s2.0-85067809024