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
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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
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
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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