Analysis of subspace iteration for eigenvalue problems with evolving matrices

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Abstract

The subspace iteration algorithm, a block generalization of the classical power iteration, is known for its excellent robustness properties. Specifically, the algorithm is resilient to variations in the original matrix, and for this reason it has played an important role in applications ranging from density functional theory in electronic structure calculations to matrix completion problems in machine learning, and subspace tracking in signal processing applications. This note explores its convergence properties in the presence of perturbations. The specific question addressed is the following. If we apply the subspace iteration algorithm to a certain matrix and this matrix is perturbed at each step, under what conditions will the algorithm converge?

Original languageEnglish (US)
Pages (from-to)103-122
Number of pages20
JournalSIAM Journal on Matrix Analysis and Applications
Volume37
Issue number1
DOIs
StatePublished - 2016

Bibliographical note

Funding Information:
Received by the editors December 30, 2014; accepted for publication (in revised form) by Z. Drmac November 13, 2015; published electronically January 28, 2016. The research of the author was supported partly by the Scientific Discovery Through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences DE-SC0008877. This work was also partly supported by NSF under grant NSF/CCF-1318597.

Publisher Copyright:
Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

  • Convergence theory
  • Density functional theory
  • Eigenvalue problems
  • Subspace iteration
  • Subspace tracking

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