H.A. van der Vorst,

Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG

for the solution of nonsymmetric linear systems,

SIAM J. Sci. Stat. Comput., Vol 13(2), pp. 631-644, 1992.

H.A. van der Vorst,

Conjugate gradient type methods for nonsymmetric linear systems,

in: R. Beauwens and P. de Groen (eds.),

" Iterative Methods in Linear Algebra" ,

Proc. of the IMACS Int. Symp. Brussels, 2-4 April 1991,

North-Holland, Amsterdam, 1992, pp. 67-76.

Henk A. van der Vorst,

Lecture notes on iterative methods,

report TR/PA/92/75, CERFACS, Toulouse, 1992.

Jack J. Dongarra and Henk A. van der Vorst,

Performance of Various Computers Using Standard Sparse Linear

Equations Solving Techniques,

Supercomputer, Vol 9(5), Sept. 1992, pp. 17-29.

Publications 1993

J. Demmel, M. Heath and H. van der Vorst,

Parallel Numerical Linear Algebra,

Acta Numerica 1993, Cambridge University Press, Cambridge,

1993, pp. 111-198.

H.A. van der Vorst, D.R. Fokkema, and G.L.G. Sleijpen,

• Further improvements in nonsymmetric hybrid iterative methods,

in "Simulation of Semiconductor Devices and Processes, Vol 5"

S. Selberherr, H. Stippel, and E. Strasser, eds., pp. 89-92,

Springer Verlag, Wien, 1993

G.L.G. Sleijpen and H.A. van der Vorst,
• Krylov subspace methods for large linear systems of equations,
Preprint 803, Department of Mathematics, University Utrecht (1993).

G.L.G. Sleijpen and H.A. van der Vorst,

• Optimal iteration methods for large linear systems of equations,

in "Numerical Methods for Advection-Diffusion Problems",

C.B. Vreugdenhil and B. Koren, eds.,

Notes on Numerical Fluid Mechanics, Vol. 45, Ch. 12, pp. 291-320,

Vieweg, Braunschweig, 1993.

H.A. van der Vorst and G.L.G. Sleijpen,

• The effect of incomplete decomposition preconditioning on the

convergence of Conjugate Gradients,

in "Incomplete Decompositions (ILU)-Algorithms, Theory, and

Applications", W. Hackbusch and G. Wittum, eds.,

Notes on Numerical Fluid Mechanics, Vol. 41, pp. 179-187,

Vieweg, Braunschweig, 1993.

Henk A. van der Vorst,

Minimum Residual Modifications to Bi-CG and Preconditioners,

in: G. Golub, A. Greenbaum, and M. Luskin (eds),

" Recent advances in iterative methods" ,

IMA Volumes in Mathematics and its Applications, Volume 60,

Springer Verlag, Berlin etc, 1993, p217-225.

Jack J. Dongarra and Henk A. van der Vorst,

Performance of Various Computers Using Standard Sparse Linear

Equations Solving Techniques,

in: J.J. Dongarra and W. Gentzsch (eds),

" Computer Benchmarks" , Advances in Parallel Computing, Volume 8,

North--Holland, Amsterdam, 1993, p177-188.

H.A. Van der Vorst and C. Vuik,

The superlinear convergence behaviour of GMRES,

Journal of Comp. and Appl. Math., Vol 48, 1993, pp. 327-341.

Henk A. Van der Vorst,

Parallel aspects of iterative methods,

in: A.E. Fincham, and B. Ford (Ed),

" Proc. IMA Conf. on Parallel Computing" ,

Oxford University Press, Oxford, UK, 1993, pp. 175-186.

Publications 1994

Richard Barrett, Michael Berry, Tony Chan, James Demmel, June Donato,

Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine,

and Henk van der Vorst,

• Templates for the solution of linear systems: Building Blocks for

Iterative Methods,

SIAM, Philadelphia, 1994.

Henk A. van der Vorst,

Recent developments in hybrid CG methods,

in: W. Gentzsch and U. Harms (Eds.),

" High Performance and Networking" ,

Proceedings International Conference, Munich, April 1994, Volume 2:

Networking and Tools, Lecture Notes in Computer Science, 797,

Springer Verlag, Berlin etc., 1994, pp. 174-183.

J.G.L. Booten, P.M. Meijer, H.J.J. te Riele and H.A. van der Vorst,

Parallel Arnoldi method for the construction of a Krylov subspace

basis: an application in magnetohydrodynamics,

in: W. Gentzsch and U. Harms (Eds.),

" High Performance and Networking" ,

Proceedings International Conference, Munich, April 1994, Volume 2:

Networking and Tools, Lecture Notes in Computer Science, 797,

Springer Verlag, Berlin etc., 1994, pp. 196-201.

E. de Sturler and H.A. van der Vorst,

Communication Cost Reduction for Krylov Methods on Parallel

Computers, in: W. Gentzsch and U. Harms (Eds.),

" High Performance and Networking" ,

Proceedings International Conference, Munich, April 1994, Volume 2:

Networking and Tools, Lecture Notes in Computer Science, 797,

Springer Verlag, Berlin etc., 1994, pp. 190-195.

S. Poedts, P.M. Meijer, J.P. Goedbloed, H.A. van der Vorst, and A. Jakoby,

Parallel Magnetohydrodynamics on the CM-5,

in: W. Gentzsch and U. Harms (Eds.),

" High Performance and Networking" ,

Proceedings International Conference, Munich, April 1994, Volume 1:

Applications, Lecture Notes in Computer Science, 796,

Springer Verlag, Berlin etc., 1994, pp. 365-370.

H.A. van der Vorst and G.L.G. Sleijpen,

An introduction to hybrid iteration methods,

in "Proceeding of the international workshop on solution techniques

for large-scale CFD problems",

W.G. Habashi, ed. (Montreal, september, 1994), pp. 143-159.

G.L.G. Sleijpen, H.A. van der Vorst, and D.R. Fokkema,

How to improve the convergence of hybrid Bi-CG methods,

in "IMACS '94, Proceedings 14the World Congress on Computation

and Applied Mathematics", W.F. Ames, ed,

Late Papers Volume, (1994), pp. 75-78.

Lianne G.C. Crone and Henk A. van der Vorst,

Communication aspects of the Conjugate Gradient method on

distributed memory machines,

Supercomputer, 58, Vol X, number 6, pp. 4--9, 1994.

J.G.L. Booten, H.A. van der Vorst, P.M. Meijer, and H.J.J. te Riele,

• A preconditioned Jacobi-Davidson method for solving large

generalized eigenvalue problems,

CWI Report NM-R9414, July 1994.

H.A. van der Vorst,

A comparison between ART, CG, and SIRT,

in "Proceedings of the Cornelius Lanczos International Centenary

Conference", J.D. Brown, M.T. Chu, D.C. Ellison, R.J. Plemmons, eds.,

Proceedings in Applied Mathematics 73, IBSN 0-89871-339-0,

SIAM, Philadelphia, 1994, pp. 302--304.

G.L.G. Sleijpen, D.R. Fokkema, and H.A. van der Vorst,

BiCGstab(ell): an Efficient and Surprisingly Stable Solver of

Nonsymmetric Linear Equations, in "Proceedings of the Cornelius

Lanczos International Centenary Conference",

J.D. Brown, M.T. Chu, D.C. Ellison, R.J. Plemmons, eds.,

Proceedings in Applied Mathematics 73, IBSN 0-89871-339-0,

SIAM, Philadelphia, 1994, pp. 291-293.

G.L.G. Sleijpen, H.A. van der Vorst, and D.R. Fokkema,

BiCGstab(ell) and other Hybrid Bi-CG Methods,

Numerical Algor., 7 (1994), pp. 75-109.

H.A. Van der Vorst and C. Vuik,

GMRESR: a Family of Nested GMRES Methods,

Numerical Linear Algebra with Applications, Vol.1(4), pp. 369-386, 1994.

Publications 1995

G.L.G. Sleijpen and H.A. van der Vorst,

An overview of approaches for the stable computation of hybrid
Bi-CG methods,

J. Applied Num. Mathematics, 19:235-254, 1995

G.L.G. Sleijpen and H.A. van der Vorst,

Hybrid Bi-Conjugate Gradient Methods for CFD Problems,

in: M. Hafez and K. Oshima (eds),

Computational Fluid Dynamics Review 1995,

Wiley, Chicester, ISBN 0 471 95589 2, 1995, pp.457-476.

G.L.G. Sleijpen and H.A. van der Vorst,

• The Jacobi-Davidson method for eigenvalue problems as an

accelerated inexact Newton scheme,

Preprint, Department of Mathematics, University Utrecht (Februari, 1995),

to appear in IMACS Conference proceedings

C.C. Paige, B.N. Parlett and H.A. Van der Vorst,

Approximate solutions and eigenvalue bounds from Krylov

subspaces, Numerical Linear Algebra with Applications, Vol 2(2),

pp. 115-134, 1995.

Z. Bai, D. Day, J. Demmel, J. Dongarra, M. Gu, A. Ruhe,

and H. van der Vorst,

• Templates for Linear Algebra Algorithms,

in: Jan van Leeuwen (Ed.), Computer Science Today: Recent Trends

and Developments, Lecture Notes in Computer Science 1000,

Springer-Verlag, Berlin etc., ISBN 3-540-60105-8, p115-140, 1995.

M.N. Kooper, H.A. van der Vorst, S. Poedts, and J.P. Goedbloed,

Application of the Implicitly Updated Arnoldi Method with a

Complex Shift and Invert Strategy in MHD,

J. of Comp. Phys., 118, pp. 320-328, 1995.

A. Booten, D. Fokkema, G. Sleijpen and H. van der Vorst,

• Jacobi-Davidson Methods for Generalized MHD-Eigenvalue

Problems, Report NM-R9514, CWI, Dept of Num Math, Amsterdam,
1995. To appear in Proc. ICIAM'95

H. A. van der Vorst and T.F. Chan,

• Parallel Preconditioning Approaches

H.A. van der Vorst,

• Computational Science Curriculum in Utrecht

H.A. van der Vorst,

• Parallel Iterative Solution Methods for Linear Systems arising

from Discretized PDE's,

in: Special Course on Parallel Computing in CFD,

AGARD-R-807, AGARD, Neuilly-sur-Seine,

France Workshop Lecture Notes

H.A. van der Vorst and G.L.G. Sleijpen,

Hybrid Iteration Solvers and their Application in CFD,

in: W.G. Habashi (ed.),

Solution Techniques for Large-Scale CFD Problems,

Wiley, Chicester, ISBN 0 471 95810 7, 1995, pp.159-175.

G.L.G. Sleijpen and H.A. van der Vorst,

Maintaining convergence properties of BiCGstab methods in

finite precision arithmetic,

Numerical Algorithms, 10, pp.203-223, 1995.

Eric de Sturler and Henk A. van der Vorst,

Reducing the effect of global communication in GMRES(m) and

CG on Parallel Distributed Memory Computers,

J. Applied Num. Math., 18:441-459, 1995.

Publications 1996

Henk A. van der Vorst,

Modern methods for the iterative solution of large systems

of linear equations, Nieuw Archief voor Wiskunde,

Vierde Serie Deel 14, 1:127-143, 1996.

Albert Booten and Henk van der Vorst,

Cracking Large-Scale Eigenvalue Computations,

Part I: Algorithms, Computers in Physics, 10:239-242, 1996.

Albert Booten and Henk van der Vorst,

Cracking Large-Scale Eigenvalue Computations,

Part II: Implementations, Computers in Physics, 10:331-334, 1996.

G.L.G. Sleijpen and H.A. van der Vorst,

A Jacobi-Davidson iteration method for linear eigenvalue problems,

SIAM J. Matrix Anal. Appl., 17:401-425, 1996.

H.J.J van Dam, J.H. van Lenthe, G.L.G. Sleijpen and H.A. van der Vorst,

An improvement of Davidson's iteration method:

Applications to MRCI and MRCEPA calculations

J. Comput. Chemistry, 17:267-272, 1996.

G.L.G. Sleijpen and H.A. van der Vorst,

Reliable updated residuals in hybrid Bi-CG methods,

Computing, 56:141-163, 1996.

Henk van der Vorst,

• Subspace Iteration for Eigenproblems,

CWI Quarterly, 9 (1 and 2):151-160, 1996.

Henk van der Vorst,

• Gedachten over de mathematisering van de samenleving

gezien `vanuit de Wiskunde' , in: Wiskunde in Nederland - Drie essays,

uitgave: Overlegcommissie Verkenningen, Amsterdam, februari 1996

(in Dutch).

H.A. van der Vorst,

Parallel Linear Solvers: Sparse Iterative Methods,

in: P. Wesseling (ed.), High Performance Computing in Fluid Dynamics,

173-200, Kluwer, Dordrecht, 1996.

D.R. Fokkema, G.L.G. Sleijpen and H.A. van der Vorst,

Generalized conjugate gradient squared,

J. Comp. and Appl. Math., 71:125-146, 1996.

G.L.G. Sleijpen, J.G.L. Booten, D.R. Fokkema and H.A. van der Vorst,

Jacobi-Davidson Type Methods for Generalized Eigenproblems

and Polynomial Eigenproblems, BIT, 36:595-633, 1996.

Gerard Sleijpen, Henk van der Vorst and Martin van Gijzen,

• Quadratic eigenproblems are no problem,

SIAM News, Vol. 29:7, September 1996, page 8-9.

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

A parallelizable and fast algorithm for very large generalized

eigenproblems, in: J. Wasniewski, J. Dongarra, K. Madsen and

D. Olesen (Eds), Applied Parallel Computing, Proceedings of PARA '96,

Lecture Notes in Computer Science 1184, Springer Verlag, Berlin,

1996, pp.686-696.

Publications 1997

M.A. Botchev, G.L.G. Sleijpen, and H.A. van der Vorst,

• Low-dimensional Krylov subspace iterations for enhancing

stability of time-step integration schemes,

Preprint 1004, Department of Mathematics, Utrecht University,

March, 1997.

Henk A. van der Vorst and Tony C. Chan,

• Linear System Solvers: Sparse iterative solvers,

in David E. Keyes, Ahmed Samed and V. Venkatakrishnan (eds),

Parallel Numerical Algorithms,

ICASE/LaRC Interdisciplinary Series in Science and

Engineering, Volume 4, Kluwer Academic, Dordecht, 1997, pp91-118.

Tony C. Chan and Henk A. van der Vorst,

• Approximate and Incomplete Factorizations,

in David E. Keyes, Ahmed Samed and V. Venkatakrishnan (eds),

Parallel Numerical Algorithms,

ICASE/LaRC Interdisciplinary Series in Science and

Engineering, Volume 4, Kluwer Academic, Dordecht, 1997, pp167-202.

G.H. Golub and H.A. van der Vorst

• Closer to the solution: iterative linear solvers,

in I.S. Duff and G.A.Watson (eds),

The State of the Art in Numerical Analysis, Clarendon Press,

Oxford, 1997, pp63-92.

Henk A. van der Vorst and Gene H. Golub

• 150 years old and still alive: eigenproblems,

in I.S. Duff and G.A. Watson (eds),

The State of the Art in Numerical Analysis, Clarendon Press,

Oxford, 1997, pp93-119.

Henk A. van der Vorst

• Iterative Methods for Linear Systems and Implementation on
  Parallel Systems,

in Raymond H. Chan, Tony F. Chan and Gene H. Golub (eds),

Iterative Methods in Scientific Computing, Springer Verlag,

Singapore, 1997, pp1-44

Publications 1998

G.L.G. Sleijpen, H.A. van der Vorst, and E. Meijerink

• Efficient expansion of subspaces in the Jacobi-Davidson method

for standard and generalized eigenproblems,

ETNA, 7:75-89, 1998

D.R. Fokkema, G.L.G. Sleijpen, and H.A. van der Vorst,

Accelerated Inexact Newton Schemes for Large Systems of

Nonlinear Equations,

SIAM J. Scient. Comput., 19:657-674, 1998

M.A. Botchev and H.A. van der Vorst

• Approximated Implicit Time-stepping Schemes
  in a Distributed Memory Parallel Environment,

Preprint 1054, Department of Mathematics, Utrecht University,

March, 1998.

Tony F. Chan, Lisette DePillis and Henk van der Vorst

• Transpose-free formulations of Lanczos-type
  methods for nonsymmetric linear systems,

Numerical Algorithms, 17, pp.51-66, 1998

D.R. Fokkema, G.L.G. Sleijpen, and H.A. van der Vorst,

Jacobi-Davidson style QR and QZ algorithms for the partial

reduction of matrix Pencils,

SIAM J. Scient. Comput., 20:94-125, 1998

J. Dongarra, I. Duff, D. Sorensen and H. van der Vorst

• Numerical Linear Algebra for
  High-Performance Computers,

SIAM, Philadelphia, PA, 1998.

Publications 1999

I.S. Duff and H.A. van der Vorst

• Developments and Trends in the Parallel

Solution of Linear Systems ,

Preprint 1091, Department of Mathematics, Utrecht University,

February, 1999.

in: Parallel Computing, Vol 25 (13-14), p.1931-1970, 1999

M.A. Botchev, G.L.G. Sleijpen and H.A. van der Vorst

• Stability control for approximate implicit
  time-stepping schemes with minimal residual iterations,

Appl. Num. Math., vol 31, pp.239-254, 1999

G.L.G. Sleijpen, H.A. van der Vorst and Z. Bai

• Jacobi-Davidson algorithms for various eigenproblems,

Preprint 1114, Dept of Math., Utrecht University, August 1999

To appear in: Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and

H. van der Vorst (editors): Templates for the Solution of

Algebraic Eigenvalue Problems: A Practical Guide.

SIAM, Philadelphia, PA, USA, 2000

Publications 2000

Henk A. van der Vorst

Krylov Subspace Iteration,

Computing in Science and Engineering,

Vol. 2(1) January/February 2000, p.32-37

Yousef Saad and Henk A. van der Vorst

• Iterative Solution of Linear Systems in the 20-th Century,

J. Comp. Appl. Math., 123, pp. 1-33, 2000.

Gene H. Golub and Henk A. van der Vorst

• Eigenvalue Computation in the 20th Century,

J. Comp. Appl. Math., 123, pp. 35-65, 2000

Henk A. van der Vorst and Qiang Ye

• Residual Replacement Strategies for Krylov Subspace Iterative
  Methods for the Convergence of True Residuals,

SIAM J. Sci. Comput., Vol. 22 (3), pp. 835-852, 2000.

Menno Genseberger, Gerard Sleijpen and Henk van der Vorst

• Using domain decomposition in the Jacobi-Davidson method,

Preprint 1164, Dept of Math., Utrecht University, October 2000

Wim Bomhof and Henk A. van der Vorst

• A Parallel linear system solver for circuit simulation problems,

Numer. Linear Algebra Appl., 7, pp. 649-665, 2000.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst

• Templates for the Solution of Algebraic Eigenvalue Problems:
  A Practical Guide.

SIAM, Philadelphia, PA, USA, 2000

A picture of the editors and some authors

M. Magolu monga Made and H. A. van der Vorst

• ParIC: A Family of Parallel Icomplete Cholesky
  Preconditioners,

in: M. Bubak, H. Afsarmanesh, R. Williams, and B. Hertzberger (Eds.),

High Performance Computing and Networking,

8th International Conference, HPCN Europe 2000, Amsterdam,

The Netherlands, May 2000, Proceedings,

Lecture Notes in Computer Science, 1823,

Springer Verlag, Berlin etc., 2000, pp. 89--98

G.L.G. Sleijpen, H.A. van der Vorst, and J. Modersitzki,

• Differences in the effects of rounding errors

in Krylov solvers for symmetric indefinite linear systems,

SIAM J. Matrix Anal. Appl., 22 (3), p. 726-751, 2000

Henk A. van der Vorst

• Solution of f(A)x=b with projection methods for the matrix A,

A. Frommer, T. Lippert, B. Medeke, and K. Schilling (editors),

Numerical Challenges in Lattice Quantum Chromodynamics,

Lecture Notes in Computational Science and Engineering. 15,

Springer Verlag, Berlin etc., 2000, pp. 18-28

J.L.M. van Dorsselaer, M.E. Hochstenbach, H.A. van der Vorst

• Computing probabilistic bounds for extreme eigenvalues
  of symmetric matrices with the Lanczos method,

SIAM J. on Matrix Anal. Appl., 22 (3), p. 837-852, 2000.

Publications 2001

M. Magolu monga Made and H.A. van der Vorst

• Parallel incomplete factorizations with pseudo-overlapped
  subdomains,

Parallel Computing, Vol. 27 (8), pp.989-1008, 2001.

M.A. Botchev and H.A. van der Vorst

• A parallel nearly implicit time-stepping scheme,

J. Comp. and Appl. Math., vol 137, pp.229-243, 2001

M. Magolu monga Made and H. A. van der Vorst

• A generalized domain decomposition paradigm for parallel incomplete
  LU factorization preconditionings,

Future generation Computer Systems, Vol. 17 (8), pp.925-932, 2001

Publications 2002

H.A. van der Vorst

• Computational Methods for large Eigenvalue Problems

in P.G. Ciarlet and J.L. Lions (eds),

Handbook of Numerical Analysis, Volume VIII,

North-Holland (Elsevier), Amsterdam 2002

pp.3-179.

M. Magolu monga Made and H. A. van der Vorst

• Spectral analysis of parallel incomplete factorizations
  with implicit pseudo-overlap,

Numerical Linear Algebra with Appl., Vol. 9 (1), pp. 45-64, 2002

Publications 2003

Henk van der Vorst

• Iterative Krylov Methods for Large Linear systems,

Cambridge University Press, Cambridge, April 2003,
ISBN: 0521818281

List of corrections

M. Hochstenbach and H. A. van der Vorst

• Alternatives to the Rayleigh quotient for the quadratic
  eigenvalue problem,

SIAM J. Sci. Comput., 25(2), p. 591-603, 2003

Publications 2004

Henk van der Vorst

• How to write a frequently-cited article ,

The Australian Mathematical Society Gazette, 31 (2), pp. 94-100, 2004