Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials

  • Authors:

  • WanZhen Liang;Roi Baer;Chandra Saravanan;Yihan Shao;Alexis T. Bell;Martin Head-Gordon

  • Affiliations:

  • Department of Chemistry, University of California, Berkeley, CA and Department of Chemical Engineering, University of California, Berkeley, CA;Department of Physical Chemistry, the Hebrew University, Jerusalem 91904, Israel;Department of Chemistry, University of California, Berkeley, CA;Department of Chemistry, University of California, Berkeley, CA;Department of Chemical Engineering, University of California, Berkeley, CA;Department of Chemistry, University of California, Berkeley, CA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

Fast and effective algorithms are discussed for resumming matrix polynomials and Chebyshev matrix polynomials. These algorithms lead to a significant speed-up in computer time by reducing the number of matrix multiplications required to roughly twice the square root of the degree of the polynomial. A few numerical tests are presented, showing that evaluation of matrix functions via polynomial expansions can be preferable when the matrix is sparse and these fast resummation algorithms are employed.