An Improved Formula for Jacobi Rotations

TL;DR

This paper introduces an enhanced algorithm for Jacobi rotations that improves the accuracy of computing eigenvalues and eigenvectors of real symmetric 2x2 matrices.

Contribution

It proposes a new, more accurate formula for Jacobi rotations, advancing numerical stability in eigenvalue computations.

Findings

Increased accuracy in eigenvalue and eigenvector calculations.

Enhanced numerical stability of the Jacobi rotation algorithm.

Potential improvements in related eigenvalue problem applications.

Abstract

We present an improved form of the algorithm for constructing Jacobi rotations. This is simultaneously a more accurate code for finding the eigenvalues and eigenvectors of a real symmetric 2x2 matrix.