A Note On Estimating the Spectral Norm of A Matrix Efficiently

TL;DR

This paper presents an efficient algorithm that combines power iteration and random sampling techniques to approximate a matrix's spectral norm with relative error, improving computational efficiency.

Contribution

The paper introduces a novel method that integrates power iteration with matrix reconstruction techniques for faster spectral norm estimation.

Findings

Achieves accurate spectral norm approximation with reduced computational cost

Combines power iteration with random sampling for efficiency

Provides theoretical guarantees on approximation quality

Abstract

We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.