Matrix perturbation bounds via contour bootstrapping

TL;DR

This paper introduces a novel 'contour bootstrapping' method to derive new matrix perturbation bounds, impacting spectral algorithms, matrix sparsification, and privacy-preserving computations.

Contribution

It presents a new perturbation analysis technique called contour bootstrapping, providing improved bounds for spectral algorithms and applications in matrix sparsification and privacy.

Findings

Derived new matrix perturbation bounds using contour bootstrapping

Provided bounds on errors in matrix sparsification for spectral computations

Discussed potential applications in privacy-preserving matrix computations

Abstract

Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds on the error occurring when one uses matrix sparsification to speed up the computation of spectral parameters. Another potential application is the estimation of the trade-off in computing with privacy.