This paper proposes a class of parallel interval matrix multisplitting AOR methods far solving systems of interval linear equations and discusses their convergence properties under the conditions that the coefficient ...This paper proposes a class of parallel interval matrix multisplitting AOR methods far solving systems of interval linear equations and discusses their convergence properties under the conditions that the coefficient matrices are interval H-matrices.展开更多
Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equations F(x) = 0. We extend the idea of nonlinear multisplitting and consider a new model ill whic...Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equations F(x) = 0. We extend the idea of nonlinear multisplitting and consider a new model ill which the iteration is executed asynchronously: Each processor calculate the solution of an individual nonlinear system belong to its nonlinear multisplitting and can update the global approximation residing in the shared memory at any time. A local convergence analysis of this model is presented. Finally, we give a uumerical example which shows a 'strange' property that speedup Sp > p and efficiency Ep > 1.展开更多
In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonover- lapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric...In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonover- lapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m opti- mization models are parallelly treated in m different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numeri- cal examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.展开更多
A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrice...A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrices of the linear systems are monotone matrices and H-matrices, respectively.展开更多
文摘This paper proposes a class of parallel interval matrix multisplitting AOR methods far solving systems of interval linear equations and discusses their convergence properties under the conditions that the coefficient matrices are interval H-matrices.
文摘Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equations F(x) = 0. We extend the idea of nonlinear multisplitting and consider a new model ill which the iteration is executed asynchronously: Each processor calculate the solution of an individual nonlinear system belong to its nonlinear multisplitting and can update the global approximation residing in the shared memory at any time. A local convergence analysis of this model is presented. Finally, we give a uumerical example which shows a 'strange' property that speedup Sp > p and efficiency Ep > 1.
文摘In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonover- lapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m opti- mization models are parallelly treated in m different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numeri- cal examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.
文摘A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrices of the linear systems are monotone matrices and H-matrices, respectively.
