Solving the 3x3 Real Symmetric Eigenproblem

TL;DR

This paper presents a specialized, efficient algorithm for solving the 3x3 real symmetric eigenproblem, optimized for high-frequency applications and GPU implementation to handle large volumes of small eigenproblems.

Contribution

It introduces a tailored, compact algorithm specifically designed for 3x3 real symmetric matrices, suitable for fast computation and GPU parallelization.

Findings

Algorithm is easily coded and compact.

Compatible with GPU-based parallel processing.

Efficiently solves large numbers of small eigenproblems.

Abstract

We develop an algorithm solving the 3x3 real symmetric eigenproblem. This is a common problem and in certain applications it must be solved many thousands of times, see for example \cite{tripref} where each element in a finite element grid generates one. Because of this it is useful to have a tailored method that is easily coded and compact. Furthermore, the method described is fully compatible with development as a GPU based code that would allow the simultaneous solution of a large number of these small eigenproblems.