关于对称矩阵${x}^TA^{-1}{x}$的估计

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2021-07-28 DOI:10.13001/ela.2021.5611

Paraskevi Fika, M. Mitrouli, Ondrej Turec

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引用次数: 1

摘要

这项工作中研究的中心数学问题是二次型$x^TA的估计^{-1}x$和向量$x\in\mathbb｛R｝^n$。估算$x^TA的几种方法^{-1}x$而不计算矩阵逆。对估计的精度进行了分析和数值分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the estimation of ${x}^TA^{-1}{x}$ for symmetric matrices

The central mathematical problem studied in this work is the estimation of the quadratic form $x^TA^{-1}x$ for a given symmetric positive definite matrix $A \in \mathbb{R}^{n \times n}$ and vector $x \in \mathbb{R}^n$. Several methods to estimate $x^TA^{-1}x$ without computing the matrix inverse are proposed. The precision of the estimates is analyzed both analytically and numerically.

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来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.