Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
On the parallel least square approaches in the krylov subspaces. / Il’in, V. P.
Supercomputing - 3rd Russian Supercomputing Days, RuSCDays 2017, Revised Selected Papers. ed. / Voevodin; S Sobolev. Vol. 793 Springer-Verlag GmbH and Co. KG, 2017. p. 168-180 (Communications in Computer and Information Science; Vol. 793).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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TY - GEN
T1 - On the parallel least square approaches in the krylov subspaces
AU - Il’in, V. P.
N1 - This work was supported by the Russian Science Foundation (project N 14-11-00485) and the Russian Foundation for Basic Research (project N 16-29-15122).
PY - 2017
Y1 - 2017
N2 - We consider different parallel versions of the least squares methods in the Krylov subspaces which are based on computing various basis vectors. These algorithms are used for solving very large real, non-symmetric, in gerenal, sparse systems of linear algebraic equations (SLAEs) which arise in grid approximations of multi-dimensional boundary value problems. In particular, the Chebyshev acceleration approach, steepest descent and minimal residual, conjugate gradient and conjugate residual are applied as preliminary iterative processes. The resulting minimization of residuals is provided by the block, or implicit, orthogonalization procedures. The properties of the Krylov approaches proposed are analysed in the “pure form”, i.e. without preconditioning. The main criteria of parallelezation are estimated. The convergence rate and stability of the algorithms are demonstated on the results of numerical experiments for the model SLAEs which present the exponential fitting approximation of diffusion-convection equations on the meshes with various steps and with different coefficients.
AB - We consider different parallel versions of the least squares methods in the Krylov subspaces which are based on computing various basis vectors. These algorithms are used for solving very large real, non-symmetric, in gerenal, sparse systems of linear algebraic equations (SLAEs) which arise in grid approximations of multi-dimensional boundary value problems. In particular, the Chebyshev acceleration approach, steepest descent and minimal residual, conjugate gradient and conjugate residual are applied as preliminary iterative processes. The resulting minimization of residuals is provided by the block, or implicit, orthogonalization procedures. The properties of the Krylov approaches proposed are analysed in the “pure form”, i.e. without preconditioning. The main criteria of parallelezation are estimated. The convergence rate and stability of the algorithms are demonstated on the results of numerical experiments for the model SLAEs which present the exponential fitting approximation of diffusion-convection equations on the meshes with various steps and with different coefficients.
KW - Block implicit least squares methods
KW - Krylov subspaces
KW - Large sparse systems of linear algebraic equations
KW - Non-symmetric matrices
KW - Numerical experiments
KW - Parallel technologies
UR - http://www.scopus.com/inward/record.url?scp=85035146320&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-71255-0_13
DO - 10.1007/978-3-319-71255-0_13
M3 - Conference contribution
AN - SCOPUS:85035146320
SN - 9783319712543
VL - 793
T3 - Communications in Computer and Information Science
SP - 168
EP - 180
BT - Supercomputing - 3rd Russian Supercomputing Days, RuSCDays 2017, Revised Selected Papers
A2 - Voevodin, null
A2 - Sobolev, S
PB - Springer-Verlag GmbH and Co. KG
T2 - 3rd Russian Supercomputing Days Conference, RuSCDays 2017
Y2 - 25 September 2017 through 26 September 2017
ER -
ID: 9673152