TY - JOUR

T1 - Parallel Variable-Triangular Iterative Methods in Krylov Subspaces

AU - Il’in, V. P.

N1 - Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/6

Y1 - 2021/6

N2 - The paper considers parallel preconditioned iterative methods in Krylov subspaces for solving systems of linear algebraic equations with large sparse symmetric positive-definite matrices resulting from grid approximations of multidimensional problems. For preconditioning, generalized block algorithms of symmetric successive over-relaxation or incomplete factorization type with matching row sums are used. Preconditioners are based on variable-triangular matrix factors with multiple alternations in triangular structure. For three-dimensional grid algebraic systems, methods are based on nested factorizations, as well as on two-level iterative processes. Successive approximations in Krylov subspaces are computed by applying a family of conjugate direction algorithms with various orthogonality and variational properties, including preconditioned conjugate gradient, conjugate residual, and minimal error methods.

AB - The paper considers parallel preconditioned iterative methods in Krylov subspaces for solving systems of linear algebraic equations with large sparse symmetric positive-definite matrices resulting from grid approximations of multidimensional problems. For preconditioning, generalized block algorithms of symmetric successive over-relaxation or incomplete factorization type with matching row sums are used. Preconditioners are based on variable-triangular matrix factors with multiple alternations in triangular structure. For three-dimensional grid algebraic systems, methods are based on nested factorizations, as well as on two-level iterative processes. Successive approximations in Krylov subspaces are computed by applying a family of conjugate direction algorithms with various orthogonality and variational properties, including preconditioned conjugate gradient, conjugate residual, and minimal error methods.

UR - http://www.scopus.com/inward/record.url?scp=85105359497&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05371-w

DO - 10.1007/s10958-021-05371-w

M3 - Article

AN - SCOPUS:85105359497

VL - 255

SP - 281

EP - 290

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 3

ER -