Smoothed analysis of componentwise condition numbers for sparse matrices
Numerical Analysis
2013-02-26 v1
Abstract
We perform a smoothed analysis of the componentwise condition numbers for determinant computation, matrix inversion, and linear equations solving for sparse n times n matrices. The bounds we obtain for the ex- pectations of the logarithm of these condition numbers are, in all three cases, of the order O(log n). As a consequence, small bounds on the smoothed loss of accuracy for triangular linear systems follow.
Cite
@article{arxiv.1302.6004,
title = {Smoothed analysis of componentwise condition numbers for sparse matrices},
author = {Dennis Cheung and Felipe Cucker},
journal= {arXiv preprint arXiv:1302.6004},
year = {2013}
}