Controlled precision QUBO-based algorithm to compute eigenvectors of symmetric matrices

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix which is based on solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices; It can compute the eigenvect...

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Bibliographic Details
Published in:PloS one 2022-01, Vol.17 (5), p.e0267954
Main Authors: Benjamin Krakoff, Susan M Mniszewski, Christian F A Negre
Format: Article
Language:English
Online Access:Get full text
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Summary:We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix which is based on solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices; It can compute the eigenvector/eigenvalue pair to essentially any arbitrary precision, and with minor modifications, can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications.
ISSN:1932-6203
DOI:10.1371/journal.pone.0267954