Search results for: Henk A. van der Vorst

Items from 1 to 9 out of 9 results

article

Preface

Zhaojun Bai, Andrew Knyazev, Henk A. van der Vorst

Linear Algebra and Its Applications > 2006 > 415 > 1 > 1-2

article

Efficient and reliable iterative methods for linear systems

Henk A. van der Vorst

Journal of Computational and Applied Mathematics > 2002 > 149 > 1 > 251-265

The approximate solutions in standard iteration methods for linear systems Ax=b, with A an n by n nonsingular matrix, form a subspace. In this subspace, one may try to construct better approximations for the solution x. This is the idea behind Krylov subspace methods. It has led to very powerful and efficient methods such as conjugate gradients, GMRES, and Bi-CGSTAB. We will give an overview of these...

article

A parallel nearly implicit time-stepping scheme

Mike A. Botchev, Henk A. van der Vorst

Journal of Computational and Applied Mathematics > 2001 > 137 > 2 > 229-243

Across-the-space parallelism still remains the most mature, convenient and natural way to parallelize large scale problems. One of the major problems here is that implicit time stepping is often difficult to parallelize due to the structure of the system. Approximate implicit schemes have been suggested to circumvent the problem (M.A. Botchev et al., Appl. Numer. Math. 31 (3) (1999) 239). These schemes...

article

Parallel incomplete factorizations with pseudo-overlapped subdomains

Mardochée Magolu monga Made, Henk A. van der Vorst

Parallel Computing > 2001 > 27 > 8 > 989-1008

We address the hard question of efficient use on parallel platforms, of incomplete factorization preconditioning techniques for solving large and sparse linear systems by Krylov subspace methods. A novel parallelization strategy based on pseudo-overlapped subdomains is explored. This results in efficient parallelizable preconditioners. Numerical results give evidence that high performance can be achieved.

article

Eigenvalue computation in the 20th century

Gene H. Golub, Henk A. van der Vorst

Journal of Computational and Applied Mathematics > 2000 > 123 > 1-2 > 35-65

This paper sketches the main research developments in the area of computational methods for eigenvalue problems during the 20th century. The earliest of such methods dates back to work of Jacobi in the middle of the 19th century. Since computing eigenvalues and vectors is essentially more complicated than solving linear systems, it is not surprising that highly significant developments in this area...

article

Iterative solution of linear systems in the 20th century

Yousef Saad, Henk A. van der Vorst

Journal of Computational and Applied Mathematics > 2000 > 123 > 1-2 > 1-33

This paper sketches the main research developments in the area of iterative methods for solving linear systems during the 20th century. Although iterative methods for solving linear systems find their origin in the early 19th century (work by Gauss), the field has seen an explosion of activity spurred by demand due to extraordinary technological advances in engineering and sciences. The past five...

article

Stability control for approximate implicit time stepping schemes with minimum residual iterations

Mikhail A. Botchev, Gerard L. G. Sleijpen, Henk A. van der Vorst

Applied Numerical Mathematics > 1999 > 31 > 3 > 239-253

Implicit schemes for the integration of ODEs are popular when stability is more of concern than accuracy, for instance for the computation of a steady state solution. However, in particular for very large systems, the solution of the involved linear systems may be very expensive. When these systems are solved iteratively to a certain tolerance, it is often not known which tolerance has to be taken...

article

Generalized conjugate gradient squared

Diederik R. Fokkema, Gerard L.G. Sleijpen, Henk A. Van der Vorst

Journal of Computational and Applied Mathematics > 1996 > 71 > 1 > 125-146

The Conjugate Gradient Squared (CGS) is an iterative method for solving nonsymmetric linear systems of equations. However, during the iteration large residual norms may appear, which may lead to inaccurate approximate solutions or may even deteriorate the convergence rate. Instead of squaring the Bi-CG polynomial as in CGS, we propose to consider products of two nearby Bi-CG polynomials which leads...

article

An overview of approaches for the stable computation of hybrid BiCG methods

Gerard L.G. Sleijpen, Henk A. van der Vorst

Applied Numerical Mathematics > 1995 > 19 > 3 > 235-254

It is well known that BiCG can be adapted so that the operations with A ^T can be avoided, and hybrid methods with computational complexity almost similar to BiCG can be constructed in a further attempt to improve the convergence behavior. Examples of this are CGS, Bi-CGSTAB, and BiCGstab(l).In many applications, the speed of convergence of these methods is very dependent on the incorporated...

Filter options

Publication date

Set your own date range

Content availability

Available (7)
None (2)

Keywords

DOMAIN DECOMPOSITION (3)
GMRES (2)
PRECONDITIONING (2)
ADI (1)
ARNOLDI'S METHOD (1)
BI-CG (1)
BI-CGSTAB (1)
BICGSTAB(L) (1)
CGS (1)
CONJUGATE GRADIENTS (1)
INCOMPLETE CHOLESKY (1)
INCOMPLETE FACTORIZATIONS (1)
ITERATIVE METHODS (1)
ITERATIVE SOLVERS (1)
JACOBI'S METHOD (1)
JACOBI-DAVIDSON (1)
KRYLOV METHODS (1)
KRYLOV SUBSPACE (1)
KRYLOV SUBSPACE METHODS (1)
LANCZOS' METHOD (1)
LARGE SPARSE LINEAR SYSTEMS (1)
MINIMUM RESIDUAL ITERATIONS (1)
MULTIGRID (1)
MULTIPROCESSOR COMPUTERS (1)
NEWTON'S METHOD (1)
NONLINEAR SYSTEMS (1)
NONSYMMETRIC LINEAR SYSTEMS (1)
PARALLEL TIME INTEGRATION (1)
PARALLELISM ACROSS THE PROBLEM (1)
PERTURBATION THEORY (1)
POLYNOMIAL ACCELERATION (1)
POWER ITERATION (1)
PRECONDITIONED CONJUGATE GRADIENT (1)
QR (1)
QZ (1)
RELAXATION METHODS (1)
RKS (1)
SOR (1)
SPARSE APPROXIMATE INVERSE (1)
SPEED UP (1)
STABILITY STEP SIZE CONTROL (1)
STIFF ODES (1)
SVD (1)
TIME STEPPING SCHEMES (1)
[AMS CLASSIFICATION CODES] 65F10 (1)
[MATHEMATICAL SUBJECT CODES] 65F15 (1)
[MATHEMATICAL SUBJECT CODES] 65M12 (1)
[MATHEMATICAL SUBJECT CODES] 65M20 (1)
[MATHEMATICAL SUBJECT CODES] 65N25 (1)
[MATHEMATICAL SUBJECT CODES] 65Y05 (1)
[MATHEMATICAL SUBJECT CODES] 68Q25 (1)
[MATHEMATICAL SUBJECT CODES] SECONDARY 65F10 (1)
more

INFONA - science communication portal

Search results for: Henk A. van der Vorst

Add recipient

Sending message cancelled

Are you sure you want to cancel sending this message?

Send message

Filter options

Publication date

Date range setting

Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.

Content availability

Keywords

Journal

Reporting an error / abuse

Sending the report failed

Accessibility options