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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&apos;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&apos;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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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