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Truncation of small matrix elements based on the Euclidean norm for blocked data structures
Author(s) -
Rubensson Emanuel H.,
Rudberg Elias,
Sałek Paweł
Publication year - 2008
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21120
Subject(s) - euclidean distance matrix , mathematics , euclidean distance , euclidean geometry , norm (philosophy) , matrix (chemical analysis) , matrix norm , lanczos resampling , invariant (physics) , unitary state , invariant subspace , unitary matrix , pure mathematics , eigenvalues and eigenvectors , quantum mechanics , mathematical physics , physics , geometry , linear subspace , materials science , political science , law , composite material
Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree–Fock and Kohn–Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary‐invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49 , 032103). The Euclidean norm is unitary‐invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009