Efficient estimates for matrix-inverse quadratic forms

Kód výsledku v 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>
Výsledek na webu
<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>

Jazyk výsledku
angličtina
Název v původním jazyce
Efficient estimates for matrix-inverse quadratic forms
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Efficient estimates for matrix-inverse quadratic forms
Popis výsledku anglicky
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.

Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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