Year: 2013
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Cheung, Dennis, Cucker, Felipe
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: City University of Hong Kong
OpenAlex ID: W2952088127