Efficient estimates for matrix-inverse quadratic forms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F25%3AA2603AX0" target="_blank" >RIV/61988987:17310/25:A2603AX0 - isvavai.cz</a>
Result on the web
<a href="https://linkinghub.elsevier.com/retrieve/pii/S0168927424000138" target="_blank" >https://linkinghub.elsevier.com/retrieve/pii/S0168927424000138</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apnum.2024.01.013" target="_blank" >10.1016/j.apnum.2024.01.013</a>

Result language
angličtina
Original language name
Efficient estimates for matrix-inverse quadratic forms
Original language description
In this paper we present two approaches for estimating matrix-inverse quadratic forms x^T A^{-1} x, where A is a symmetric positive definite matrix of order n, and x in R^n. Using the first, analytic approach, we establish two families of estimates which are convenient for matrices with small condition number. Based on the second, heuristic approach, we derive two families of estimates which are suitable for matrices when vector x is close enough to an eigenvector. The low complexity and stability of the estimates is proved. Several numerical results illustrating the effectiveness of the methods are presented.
Czech name
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Czech description
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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
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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