Rational approximation to the Fermi-Dirac function with applications in density functional theory

Roger B. Sidje, Yousef Saad

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We are interested in computing the Fermi-Dirac matrix function in which the matrix argument is the Hamiltonian matrix arising from density functional theory (DFT) applications. More precisely, we are really interested in the diagonal of this matrix function. We discuss rational approximation methods to the problem, specifically the rational Chebyshev approximation and the continued fraction representation. These schemes are further decomposed into their partial fraction expansions, leading ultimately to computing the diagonal of the inverse of a shifted matrix over a series of shifts. We describe Lanczos and sparse direct methods to address these systems. Each approach has advantages and disadvantages that are illustrated with experiments.

Original languageEnglish (US)
Pages (from-to)455-479
Number of pages25
JournalNumerical Algorithms
Volume56
Issue number3
DOIs
StatePublished - Mar 1 2011

Keywords

  • Continued fraction
  • Density functional theory
  • Diagonal of matrix inverse
  • Electronic structure calculations
  • Fermi-Dirac
  • Rational Chebyshev

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