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A submatrix algorithm for the matrix‐vector multiplication of very large matrices
Author(s) -
Lindh Roland,
Malmquist PerÅrke
Publication year - 1989
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.540100307
Subject(s) - supermatrix , matrix multiplication , matrix (chemical analysis) , partition (number theory) , multiplication (music) , algorithm , multiplication algorithm , fock matrix , mathematics , formalism (music) , computer science , parallel computing , algebra over a field , arithmetic , fock space , combinatorics , pure mathematics , physics , quantum mechanics , chemistry , current algebra , chromatography , affine lie algebra , binary number , quantum , art , musical , visual arts
Abstract In self‐consistent field (SCF) calculations the construction of the Fock matrix is most time‐consuming step. The Fock matrix construction may formally be seen as a matrix‐vector multiplication, where the matrix is the supermatrix, ijkl , and the vector is the first‐order density matrix, γ ij . This formalism should be optimal for vector machines. This is not, however, fully utilized in most programs running on computers with small core memory. The size of the matrix, typically in the order of 10 6 –10 8 elements, has forced programmers to implement other nonvectorizable methods. We will present a submatrixbased algorithm which will partition the supermatrix so that vectorizable methods can be employed. The method will also reduce the input/output.