Backward Stability of the Schur Canonical Form

TL;DR

This paper proves that the Schur decomposition of a matrix remains stable under small perturbations, ensuring reliable numerical computations in linear algebra.

Contribution

It establishes the backward stability of the Schur canonical form, a key result for numerical analysis of matrix decompositions.

Findings

Schur decomposition is backward stable under small perturbations

Provides theoretical guarantees for numerical algorithms involving Schur form

Enhances confidence in computational methods using Schur decomposition

Abstract

In the present paper, we show the backward stability of the Schur decomposition for a given matrix under small perturbation.