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Using the PRIMME eigensolver in materials science applications
Author(s) -
Stathopoulos Andreas
Publication year - 2006
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200666813
Subject(s) - eigenvalues and eigenvectors , orthogonality , quadratic growth , dimension (graph theory) , software , computational science , computation , computer science , hermitian matrix , scale (ratio) , mathematics , algorithm , pure mathematics , physics , geometry , programming language , quantum mechanics
One of the outstanding computational problems in materials science is the solution of large, Hermitian eigenvalue problems. The dimension of these problems can grow to several millions, while thousands of eigenvalues and eigenvectors must be computed. Applications that must maintain orthogonality in the eigenvector basis scale quadratically to the number of eigenvectors. In this paper, we present an overview of the state‐of‐the‐art in methods and software for eigenvalue computations, and demonstrate why our new package PRIMME fills an important gap in both methods and software. Moreover, we show that PRIMME includes two nearly optimal methods, and that it can be significantly faster than any existing method. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)