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

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  • Benjamin Krakoff
  • Susan M Mniszewski
  • Christian F A Negre

Abstract

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.

Suggested Citation

  • Benjamin Krakoff & Susan M Mniszewski & Christian F A Negre, 2022. "Controlled precision QUBO-based algorithm to compute eigenvectors of symmetric matrices," PLOS ONE, Public Library of Science, vol. 17(5), pages 1-15, May.
    • Handle: RePEc:plo:pone00:0267954
    DOI: 10.1371/journal.pone.0267954
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    References listed on IDEAS

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    1. Gary Kochenberger & Fred Glover & Bahram Alidaee & Cesar Rego, 2005. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem," Annals of Operations Research, Springer, vol. 139(1), pages 229-241, October.
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