Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials

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

doi:10.1016/j.jcp.2003.08.027

Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials

Wan Zhen Liang, Roi Baer, Chandra Saravanan, Yihan Shao, Alexis T. Bell, Martin Head-Gordon^*

^*Corresponding author for this work

Institute of Chemistry

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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.

Original language	English
Pages (from-to)	575-587
Number of pages	13
Journal	Journal of Computational Physics
Volume	194
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2003.08.027
State	Published - 1 Mar 2004

Bibliographical note

Funding Information:
WZL would like to express her deep gratitude to Prof. Arup K. Chakraborty and Mr. Baron Peters for many stimulating discussions relevant to this work. Financial support from BP (WZL) and the Israel-US Binational Science Foundation (Baer & MHG) as well as support (MHG) from the National Science Foundation (CHE-9981997) are gratefully acknowledged. This work was also supported by funding from Q-Chem Inc via an SBIR subcontract from the National Institutes of Health (R43GM069255-01). MHG is a part owner of Q-Chem Inc.

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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.",

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AU - Bell, Alexis T.

AU - Head-Gordon, Martin

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Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials

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