A homotopy method for finding eigenvalues and eigenvectors
Kerry M. Soileau
TL;DR
This paper introduces a homotopy method that leverages solutions from a nearby operator to efficiently compute eigenvalues and eigenvectors of a target operator.
Contribution
It presents a novel homotopy approach for eigenvalue problems, connecting solutions of similar operators to facilitate computation.
Findings
Provides a homotopy-based algorithm for eigenvalue computation
Demonstrates effectiveness in linking solutions of related operators
Offers potential computational advantages over traditional methods
Abstract
Suppose we want to find the eigenvalues and eigenvectors for the linear operator L, and suppose that we have solved this problem for some other "nearby" operator K. In this paper we show how to represent the eigenvalues and eigenvectors of L in terms of the corresponding properties of K.
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Taxonomy
TopicsIterative Methods for Nonlinear Equations · Matrix Theory and Algorithms · Advanced Optimization Algorithms Research