Year: 2008
Type: preprint
Abstract: We consider the following problem: Given a matrix A, find minimal subsets of columns of A with cardinality no larger than a given bound that are linear dependent or nearly so. This problem arises in various forms in optimization, electrical engineering, and statistics. In its full generality, the problem is known to be NP-complete. We present a Monte Carlo method that finds such subsets with high confidence. We also give a deterministic method that is capable of proving that no subsets of linearly dependent columns up to a certain cardinality exist. The performance of both methods is analyzed and illustrated with numerical experiments.
Source: arXiv (Cornell University)
Author: Engler, Hans
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1603830546