A class of asynchronous multisplitting two-stage iterations for large sparse block systems of weakly nonlinear equations

TY - JOUR

T1 - A class of asynchronous multisplitting two-stage iterations for large sparse block systems of weakly nonlinear equations

AU - Bai, Zhong Z.

AU - Evans, D. J.

AU - Calinescu, R. C.

PY - 1999/10/30

Y1 - 1999/10/30

N2 - For the block system of weakly nonlinear equations Ax=G(x), where A∈Rn×n is a large sparse block matrix and G:Rn→Rn is a block nonlinear mapping having certain smoothness properties, we present a class of asynchronous parallel multisplitting block two-stage iteration methods in this paper. These methods are actually the block variants and generalizations of the asynchronous multisplitting two-stage iteration methods studied by Bai and Huang (Journal of Computational and Applied Mathematics 93(1) (1998)13-33), and they can achieve high parallel efficiency of the multiprocessor system, especially, when there is load imbalance. Under quite general conditions that A∈Rn×n is a block H-matrix of different types and G:Rn→Rn is a block P-bounded mapping, we establish convergence theories of these asynchronous multisplitting block two-stage iteration methods. Numerical computations show that these new methods are very efficient for solving the block system of weakly nonlinear equations in the asynchronous parallel computing environment.

AB - For the block system of weakly nonlinear equations Ax=G(x), where A∈Rn×n is a large sparse block matrix and G:Rn→Rn is a block nonlinear mapping having certain smoothness properties, we present a class of asynchronous parallel multisplitting block two-stage iteration methods in this paper. These methods are actually the block variants and generalizations of the asynchronous multisplitting two-stage iteration methods studied by Bai and Huang (Journal of Computational and Applied Mathematics 93(1) (1998)13-33), and they can achieve high parallel efficiency of the multiprocessor system, especially, when there is load imbalance. Under quite general conditions that A∈Rn×n is a block H-matrix of different types and G:Rn→Rn is a block P-bounded mapping, we establish convergence theories of these asynchronous multisplitting block two-stage iteration methods. Numerical computations show that these new methods are very efficient for solving the block system of weakly nonlinear equations in the asynchronous parallel computing environment.

KW - 65H10

KW - 65W05

KW - Asynchronous parallel method

KW - Block system of weakly nonlinear equations

KW - Convergence theory

KW - CR: G1.3

KW - Matrix multisplitting

KW - Block two-stage interation

KW - Block H-matrix

UR - http://www.scopus.com/inward/record.url?scp=0033365539&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(99)00236-8

DO - 10.1016/S0377-0427(99)00236-8

M3 - Article

AN - SCOPUS:0033365539

VL - 110

SP - 271

EP - 286

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -