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Henk van der Vorst

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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[14] and one of the authors of the Templates projects for linear problems[15] and eigenproblems.[16]

Discover more about Henk van der Vorst related topics

Utrecht University

Utrecht University

Utrecht University is a public research university in Utrecht, Netherlands. Established 26 March 1636, it is one of the oldest universities in the Netherlands. In 2018, it had an enrollment of 31,801 students, and employed 7,191 faculty and staff. In 2018, 525 PhD degrees were awarded and 6,948 scientific articles were published. The 2018 budget of the university was €857 million.

Institute for Scientific Information

Institute for Scientific Information

The Institute for Scientific Information (ISI) was an academic publishing service, founded by Eugene Garfield in Philadelphia in 1956. ISI offered scientometric and bibliographic database services. Its specialty was citation indexing and analysis, a field pioneered by Garfield.

Biconjugate gradient stabilized method

Biconjugate gradient stabilized method

In numerical linear algebra, the biconjugate gradient stabilized method, often abbreviated as BiCGSTAB, is an iterative method developed by H. A. van der Vorst for the numerical solution of nonsymmetric linear systems. It is a variant of the biconjugate gradient method (BiCG) and has faster and smoother convergence than the original BiCG as well as other variants such as the conjugate gradient squared method (CGS). It is a Krylov subspace method. Unlike the original BiCG method, it doesn't require multiplication by the transpose of the system matrix.

Royal Netherlands Academy of Arts and Sciences

Royal Netherlands Academy of Arts and Sciences

The Royal Netherlands Academy of Arts and Sciences is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam.

Order of the Netherlands Lion

Order of the Netherlands Lion

The Order of the Netherlands Lion, also known as the Order of the Lion of the Netherlands is a Dutch order of chivalry founded by King William I of the Netherlands on 29 September 1815.

Society for Industrial and Applied Mathematics

Society for Industrial and Applied Mathematics

Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics.

Preconditioner

Preconditioner

In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method.

Krylov subspace

Krylov subspace

In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under the first r powers of A, that is,

Nonlinear eigenproblem

Nonlinear eigenproblem

In mathematics, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the (ordinary) eigenvalue problem to equations that depend nonlinearly on the eigenvalue. Specifically, it refers to equations of the form

Conjugate gradient method

Conjugate gradient method

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems.

Lanczos algorithm

Lanczos algorithm

The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the "most useful" eigenvalues and eigenvectors of an Hermitian matrix, where is often but not necessarily much smaller than . Although computationally efficient in principle, the method as initially formulated was not useful, due to its numerical instability.

Neumann series

Neumann series

A Neumann series is a mathematical series of the form

Source: "Henk van der Vorst", Wikipedia, Wikimedia Foundation, (2022, November 25th), https://en.wikipedia.org/wiki/Henk_van_der_Vorst.

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References
  1. ^ Prof.dr. H.A. van der Vorst at the Catalogus Professorum Academiæ Rheno-Traiectinæ
  2. ^ 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
  3. ^ in-cites, September 2001, 2001
  4. ^ "Henk van der Vorst" (in Dutch). Royal Netherlands Academy of Arts and Sciences. Retrieved 14 July 2015.
  5. ^ Members of the Netherlands Academy of Technology and Innovation, archived from the original on 2011-07-24
  6. ^ Jan Brandts; Bernd Fischer; Andy Wathen (December 2006), "Reflections on Sir Henk van der Vorst", SIAM News, 39 (10)
  7. ^ "SIAM Fellows: Class of 2009". SIAM. Retrieved 2009-12-18.
  8. ^ 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
  9. ^ 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
  10. ^ 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
  11. ^ 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
  12. ^ 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
  13. ^ H.A. van der Vorst (1989), "High performance preconditioning", SIAM J. Sci. Stat. Comput., 10 (6): 1174–1185, doi:10.1137/0910071
  14. ^ H.A. van der Vorst (April 2003), Iterative Krylov Methods for Large Linear systems, Cambridge University Press, Cambridge, ISBN 978-0-521-81828-5
  15. ^ 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
  16. ^ 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 2008
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