On Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems

Details On Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems On Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems

2003-09-17

arxiv.org/abs/math/0309278v1

Mathematics

Numerical Analysis

31 pages

Scientific paper

In this paper we study the distribution tails and the moments of a condition number which arises in the study of homogeneous systems of linear inequalities. We consider the case where this system is defined by a Gaussian random matrix and characterise the exact decay rates of the distribution tails, improve the existing moment estimates, and prove various limit theorems for large scale systems. Our results are of complexity theoretic interest, because interior-point methods and relaxation methods for the solution of systems of linear inequalities have running times that are bounded in terms of the logarithm and the square of the condition number respectively.

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