Inflation of poorly conditioned zeros of systems of analytic functions

TL;DR

This paper introduces a method called inflation to transform systems of analytic functions with poorly conditioned zeros into systems with well-conditioned zeros, aiding in isolating clusters of zeros.

Contribution

It proposes a novel inflation technique that regularizes zeros of analytic systems, improving zero isolation methods.

Findings

Effective zero regularization through inflation

Enhanced zero cluster isolation capability

Applicable to systems with poorly conditioned zeros

Abstract

Given a system of analytic functions and an approximate zero, we introduce inflation to transform this system into one with a regular quadratic zero. This leads to a method for isolating a cluster of zeros of the given system.