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Efficient calculation of a normal matrix–vector product for anisotropic full‐matrix least‐squares refinement of macromolecular structures
Author(s) -
Strokopytov Boris V.
Publication year - 2009
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889809040989
Subject(s) - matrix (chemical analysis) , conjugate gradient method , algorithm , normal matrix , square matrix , anisotropy , fourier transform , normal , product (mathematics) , mathematics , computer science , mathematical analysis , physics , geometry , symmetric matrix , materials science , eigenvalues and eigenvectors , optics , quantum mechanics , surface (topology) , composite material
A novel algorithm is described for multiplying a normal equation matrix by an arbitrary real vector using the fast Fourier transform technique during anisotropic crystallographic refinement. The matrix–vector algorithm allows one to solve normal matrix equations using the conjugate‐gradients or conjugate‐directions technique without explicit calculation of a normal matrix. The anisotropic version of the algorithm has been implemented in a new version of the computer program FMLSQ . The updated program has been tested on several protein structures at high resolution. In addition, rapid methods for preconditioner and normal matrix–vector product calculations are described.