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 -