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

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