Condition Estimation by Means of the Power Method

TL;DR

This paper presents a technique to estimate a matrix's condition number using the Power Method, which involves iterative matrix-vector multiplications, offering a potentially efficient alternative to traditional methods.

Contribution

It introduces a novel approach to condition number estimation based on the Power Method, expanding the toolkit for numerical linear algebra analysis.

Findings

Demonstrates the effectiveness of the Power Method for condition estimation.

Provides theoretical analysis of convergence properties.

Shows potential computational advantages over existing methods.

Abstract

We estimate the condition number of a matrix by applying the Power Method, that is essentially a sequence of matrix-by-vector multiplications, similarly to the Lanczos method.