# On local analysis

## TL;DR

This paper extends smoothed analysis estimates for condition numbers to Gaussian distributions and introduces a local analysis concept to study their behavior around specific points.

## Contribution

It provides a Gaussian extension of smoothed analysis estimates and introduces a new local analysis framework for condition numbers.

## Key findings

- Extended smoothed analysis estimates to Gaussian distributions.
- Introduced a local analysis notion for condition numbers.
- Captured behavior of condition numbers around specific points.

## Abstract

We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these condition numbers around a point.