Solving Linear Problems with Finite Precision III: Sharp Expectation Bounds

TL;DR

This paper establishes an O(log n) bound on the expected logarithm of the condition number for linear program optimizers, advancing understanding of finite precision effects in linear problem solving.

Contribution

It provides a sharp expectation bound for the condition number in linear programming, improving theoretical insights into numerical stability.

Findings

Proves an O(log n) bound on the expectation of log condition number

Enhances understanding of finite precision impacts in linear optimization

Offers theoretical guarantees for numerical stability in linear programming

Abstract

We prove an O(log n) bound for the expectation of the logarithm of the condition number K for the computation of optimizers of linear programs.