Year: 2011
Type: preprint
Abstract: A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale's $γ$-Theorem is proven. The main result of this paper bounds the complexity of path-following methods in terms of the length of the path in the condition metric.
Source: arXiv (Cornell University)
Author: Armentano, Diego
Institution: Universidad de la República de Uruguay
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952058691