His major contributions include preconditioned iterative methods, in particular the ICCG (incomplete Cholesky conjugate gradient) method (developed together with Koos Meijerink), a version of preconditioned conjugate gradient method,[8][9] the BiCGSTAB[2] and (together with Kees Vuik) GMRESR[10]Krylov subspace methods and (together with Gerard Sleijpen) the Jacobi-Davidson method[11] for solving ordinary, generalized, and nonlineareigenproblems. He has analyzed convergence behavior of the conjugate gradient[12] and Lanczos methods. He has also developed a number of preconditioners for parallel computers,[13] including truncated Neumann series preconditioner, incomplete twisted factorizations, and the incomplete factorization based on the so-called "vdv" ordering.
He is the author of the book Iterative Krylov Methods for Large Linear systems[14] and one of the authors of the Templates projects for linear problems[15] and eigenproblems.[16]
Referencesedit
^Prof.dr. H.A. van der Vorst at the Catalogus Professorum Academiæ Rheno-Traiectinæ
^ ab H.A. van der Vorst (1992), "Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems", SIAM J. Sci. Stat. Comput., 13 (2): 631–644, doi:10.1137/0913035, hdl:10338.dmlcz/104566
^Jan Brandts; Bernd Fischer; Andy Wathen (December 2006), "Reflections on Sir Henk van der Vorst", SIAM News, 39 (10)
^ "SIAM Fellows: Class of 2009". SIAM. Retrieved 2009-12-18.
^ J.A. Meijerink; H.A.van der Vorst (1977), "An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix", Math. Comp., 31 (137): 148–162, doi:10.2307/2005786, JSTOR 2005786
^ H.A. van der Vorst (1981), "Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems", J. Comput. Phys., 44 (1): 1–19, Bibcode:1981JCoPh..44....1V, doi:10.1016/0021-9991(81)90034-6
^ H.A. van der Vorst; C. Vuik (1994), "GMRESR: A family of nested GMRES methods", Numer. Lin. Alg. Appl., 1 (4): 369–386, CiteSeerX10.1.1.465.4477, doi:10.1002/nla.1680010404
^ G.L.G. Sleijpen; H.A. van der Vorst (1996), "A Jacobi-Davidson iteration method for linear eigenvalue problems", SIAM J. Matrix Anal. Appl., 17 (2): 401–425, CiteSeerX10.1.1.50.2569, doi:10.1137/S0895479894270427
^ A. van der Sluis; H.A. van der Vorst (1986), "The rate of convergence of conjugate gradients", Numerische Mathematik, 48 (5): 543–560, doi:10.1007/BF01389450, S2CID 122190605
^ H.A. van der Vorst (1989), "High performance preconditioning", SIAM J. Sci. Stat. Comput., 10 (6): 1174–1185, doi:10.1137/0910071
^ H.A. van der Vorst (April 2003), Iterative Krylov Methods for Large Linear systems, Cambridge University Press, Cambridge, ISBN978-0-521-81828-5
^ Barrett, Richard; Berry, Michael W.; Chan, Tony F.; Demmel, James; Donato, June; Dongarra, Jack; Eijkhout, Victor; Pozo, Roldan; Romine, Charles; Vorst, Henk van der (January 1994), Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, ISBN978-0-89871-328-2, retrieved 1 January 2008
^ Bai, Zhaojun; Demmel, James; Dongarra, Jack; Ruhe, Axel; Vorst, Henk van der (January 2000), Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide, ISBN978-0-89871-471-5, retrieved 1 January 2008
External linksedit
Home page of Henk van der Vorst at Utrecht University (Accessed December 2009)
Private homepage of Henk van der Vorst (Accessed December 2009)
henk, vorst, this, dutch, name, surname, vorst, vorst, hendrik, henk, albertus, vorst, born, 1944, venlo, dutch, mathematician, emeritus, professor, numerical, analysis, utrecht, university, according, institute, scientific, information, paper, bicgstab, metho. In this Dutch name the surname is van der Vorst not Vorst Hendrik Henk Albertus van der Vorst born 5 May 1944 Venlo 1 is a Dutch mathematician and Emeritus Professor of Numerical Analysis at Utrecht University According to the Institute for Scientific Information ISI his paper 2 on the BiCGSTAB method was the most cited paper in the field of mathematics in the 1990s 3 He is a member of the Royal Netherlands Academy of Arts and Sciences KNAW since 2002 4 and the Netherlands Academy of Technology and Innovation 5 In 2006 he was awarded a knighthood of the Order of the Netherlands Lion 6 Henk van der Vorst is a Fellow of Society for Industrial and Applied Mathematics SIAM 7 His major contributions include preconditioned iterative methods in particular the ICCG incomplete Cholesky conjugate gradient method developed together with Koos Meijerink a version of preconditioned conjugate gradient method 8 9 the BiCGSTAB 2 and together with Kees Vuik GMRESR 10 Krylov subspace methods and together with Gerard Sleijpen the Jacobi Davidson method 11 for solving ordinary generalized and nonlinear eigenproblems He has analyzed convergence behavior of the conjugate gradient 12 and Lanczos methods He has also developed a number of preconditioners for parallel computers 13 including truncated Neumann series preconditioner incomplete twisted factorizations and the incomplete factorization based on the so called vdv ordering He is the author of the book Iterative Krylov Methods for Large Linear systems 14 and one of the authors of the Templates projects for linear problems 15 and eigenproblems 16 References edit Prof dr H A van der Vorst at the Catalogus Professorum Academiae Rheno Traiectinae a b H A van der Vorst 1992 Bi CGSTAB A fast and smoothly converging variant of Bi CG for the solution of nonsymmetric linear systems SIAM J Sci Stat Comput 13 2 631 644 doi 10 1137 0913035 hdl 10338 dmlcz 104566 in cites September 2001 2001 Henk van der Vorst in Dutch Royal Netherlands Academy of Arts and Sciences Retrieved 14 July 2015 Members of the Netherlands Academy of Technology and Innovation archived from the original on 2011 07 24 Jan Brandts Bernd Fischer Andy Wathen December 2006 Reflections on Sir Henk van der Vorst SIAM News 39 10 SIAM Fellows Class of 2009 SIAM Retrieved 2009 12 18 J A Meijerink H A van der Vorst 1977 An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M Matrix Math Comp 31 137 148 162 doi 10 2307 2005786 JSTOR 2005786 H A van der Vorst 1981 Iterative solution methods for certain sparse linear systems with a non symmetric matrix arising from PDE problems J Comput Phys 44 1 1 19 Bibcode 1981JCoPh 44 1V doi 10 1016 0021 9991 81 90034 6 H A van der Vorst C Vuik 1994 GMRESR A family of nested GMRES methods Numer Lin Alg Appl 1 4 369 386 CiteSeerX 10 1 1 465 4477 doi 10 1002 nla 1680010404 G L G Sleijpen H A van der Vorst 1996 A Jacobi Davidson iteration method for linear eigenvalue problems SIAM J Matrix Anal Appl 17 2 401 425 CiteSeerX 10 1 1 50 2569 doi 10 1137 S0895479894270427 A van der Sluis H A van der Vorst 1986 The rate of convergence of conjugate gradients Numerische Mathematik 48 5 543 560 doi 10 1007 BF01389450 S2CID 122190605 H A van der Vorst 1989 High performance preconditioning SIAM J Sci Stat Comput 10 6 1174 1185 doi 10 1137 0910071 H A van der Vorst April 2003 Iterative Krylov Methods for Large Linear systems Cambridge University Press Cambridge ISBN 978 0 521 81828 5 Barrett Richard Berry Michael W Chan Tony F Demmel James Donato June Dongarra Jack Eijkhout Victor Pozo Roldan Romine Charles Vorst Henk van der January 1994 Templates for the Solution of Linear Systems Building Blocks for Iterative Methods ISBN 978 0 89871 328 2 retrieved 1 January 2008 Bai Zhaojun Demmel James Dongarra Jack Ruhe Axel Vorst Henk van der January 2000 Templates for the Solution of Algebraic Eigenvalue Problems a Practical Guide ISBN 978 0 89871 471 5 retrieved 1 January 2008External links editHome page of Henk van der Vorst at Utrecht University Accessed December 2009 Private homepage of Henk van der Vorst Accessed December 2009 Henk van der Vorst at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Henk van der Vorst amp oldid 1189691662, wikipedia, wiki, book, books, library,
