摘要:

AbstractThe parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two‐dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE‐2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large syst

ISSN:1070-5325    

DOI:10.1002/nla.1680020102

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe incomplete Cholesky decomposition is known as an excellent smoother in a multigrid iteration and as a preconditioner for the conjugate gradient method. However, the existence of the decomposition is only ensured if the system matrix is an M‐matrix. It is well‐known that finite element methods usually do not lead to M‐matrices. In contrast to this restricting fact, numerical experiments show that, even in cases where the system matrix is not an M‐matrix the behaviour of the incomplete Cholesky decomposition apparently does not depend on the structure of the grid. In this paper the behaviour of the method is investigated theoretically for a model problem, where the M‐matrix condition is violated systematically by a suitable perturbation. It is shown that in this example the stability of the incomplete Cholesky decomposition is independent of the perturbation and that the analysis of the smoothing property can be carried through. This can be considered as a generalization of the results for the so called square‐grid triangulation, as has been established by Wittum in [1

ISSN:1070-5325    

DOI:10.1002/nla.1680020103

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this paper, a new backward error criterion, together with a sensitivity measure, is presented for assessing solution accuracy of nonsymmetric and symmetric algebraic Riccati equations (AREs). The usual approach to assessing reliability of computed solutions is to employ standard perturbation and sensitivity results for linear systems and to extend them further to AREs. However, such methods are not altogether appropriate since they do not take account of the underlying structure of these matrix equations. The approach considered here is to first compute the backward error of a computed solution X̂ that measures the amount by which data must be perturbed so that X̂ is the exact solution of the perturbed original system. Conventional perturbation theory is used to define structured condition numbers that fully respect the special structure of these matrix equations. The new condition number, together with the backward error of computed solutions, provides accurate estimates for the sensitivity of solutions. Optimal perturbations are then used in an iterative refinement procedure to give further more accurate approximations of actual solutions. The results are derived in their most general setting for nonsymmetric and symmetric AREs. This in turn offers a unifying framework through which it is possible to establish similar results for Sylvester equations, Lyapunov equations, linear systems, and matrix inversion

ISSN:1070-5325    

DOI:10.1002/nla.1680020104

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe paper considers a possible approach to the construction of high‐quality preconditionings for solving large sparse unsymmetric offdiagonally dominant, possibly indefinite linear systems. We are interested in the construction of an efficient iterative method which does not require from the user a prescription of several problem‐dependent parameters to ensure the convergence, which can be used in the case when only a procedure for multiplying the coefficient matrix by a vector is available and which allows for an efficient parallel/vector implementation with only one additional assumption that the most of eigenvalues of the coefficient matrix are condensed in a vicinity of the point 1 of the complex plane. The suggested preconditioning strategy is based on consecutive translations of groups of spread eigenvalues into a vicinity of the point 1. Approximations to eigenvalues to be translated are computed by the Arnoldi procedure at several GMRES(k) iterations. We formulate the optimization problem to find optimal translations, present its suboptimal solution and prove the numerical stability of consecutive translations. The results of numerical experiments with the model CFD problem show the efficiency of the suggested preconditioning strat

ISSN:1070-5325    

DOI:10.1002/nla.1680020105

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:1070-5325    

DOI:10.1002/nla.1680020106

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:1070-5325    

DOI:10.1002/nla.1680020101

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY