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

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Paraskevi Fika
Marilena Mitrouli
Ondrej Turek

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.


 

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