Open AccessModified method of parallel matrix sweep
Author(s) -
A. A. Zgirouski,
Н. А. Лиходед
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2019-55-4-425-434
Subject(s) - tridiagonal matrix , tridiagonal matrix algorithm , linear system , block (permutation group theory) , matrix (chemical analysis) , computation , system of linear equations , sparse matrix , computer science , stability (learning theory) , algorithm , mathematics , block matrix , parallel computing , mathematical optimization , eigenvalues and eigenvectors , mathematical analysis , physics , geometry , materials science , quantum mechanics , machine learning , composite material , gaussian
The topic of this paper refers to efficient parallel solvers of block-tridiagonal linear systems of equations. Such systems occur in numerous modeling problems and require usage of high-performance multicore computation systems. One of the widely used methods for solving block-tridiagonal linear systems in parallel is the original block-tridiagonal sweep method. We consider the algorithm based on the partitioning idea. Firstly, the initial matrix is split into parts and transformations are applied to each part independently to obtain equations of a reduced block-tridiagonal system. Secondly, the reduced system is solved sequentially using the classic Thomas algorithm. Finally, all the parts are solved in parallel using the solutions of a reduced system. We propose a modification of this method. It was justified that if known stability conditions for the matrix sweep method are satisfied, then the proposed modification is stable as well.