Symmetric matrix inversion using modified Gaussian elimination

TL;DR

This paper introduces two novel symmetric matrix inversion methods based on modified Gaussian elimination that avoid square root calculations, are computationally efficient, and applicable to all non-singular symmetric matrices.

Contribution

The paper presents two new variants of symmetric matrix inversion methods that are more efficient and versatile than existing techniques, avoiding square root computations.

Findings

Methods successfully invert symmetric matrices without square roots

Simulation confirms efficiency and broad applicability

Applicable to any non-singular symmetric matrices

Abstract

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of them can be used efficiently not only for positive (semi-) definite, but for any non-singular symmetric matrix inversion. We use simulation to verify results, which represented in this paper.