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

IF 0.7 4区 数学 Q2 Mathematics
Paraskevi Fika, M. Mitrouli, Ondrej Turec
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引用次数: 1

Abstract

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.  
关于对称矩阵${x}^TA^{-1}{x}$的估计
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。
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
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.
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