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Estimating the Quadratic Form x^T A^{-m} x for Symmetric Matrices: Further Progress and Numerical Computations

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F21%3AA2202AMY" target="_blank" >RIV/61988987:17310/21:A2202AMY - isvavai.cz</a>

  • Result on the web

    <a href="https://www.mdpi.com/2227-7390/9/12/1432/htm" target="_blank" >https://www.mdpi.com/2227-7390/9/12/1432/htm</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.3390/math9121432" target="_blank" >10.3390/math9121432</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Estimating the Quadratic Form x^T A^{-m} x for Symmetric Matrices: Further Progress and Numerical Computations

  • Original language description

    In the present work we study estimates for quadratic forms of the type $x^T A^{-m} x$, $min mathbb{N}$, for symmetric matrices. We derive a general approach for estimating this type of quadratic forms and we present some upper bounds for the corresponding absolute error. Specifically, we consider three different approaches for estimating the quadratic form $x^T A^{-m} x$. The first approach is based on a projection method, the second one is a minimization procedure and the last approach is heuristic. Numerical examples showing the effectiveness of the estimates are presented. Furthermore, we compare the behaviour of the proposed estimates with other methods which are derived in the literature.

  • 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

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Mathematics

  • ISSN

    2227-7390

  • e-ISSN

  • Volume of the periodical

    9

  • Issue of the periodical within the volume

    12

  • Country of publishing house

    CH - SWITZERLAND

  • Number of pages

    13

  • Pages from-to

    1-13

  • UT code for WoS article

    000666533900001

  • EID of the result in the Scopus database

    2-s2.0-85109036510