Complexity of Path-Following Methods for the Eigenvalue Problem

Details Complexity of Path-Following Methods for the Eigenvalue Problem Complexity of Path-Following Methods for the Eigenvalue Problem

2011-08-13

arxiv.org/abs/1108.2828v1

Mathematics

Numerical Analysis

Scientific paper

In this paper we study path-following methods for the eigenvalue problem. We
introduce a projective framework to analyze this problem. We define a condition
number and a Newton's map appropriate for this context, proving a version of
the $\gamma$-Theorem. Our main result bounds the complexity of path-following
methods in terms of the length of the path in the condition metric.

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