Henk van der Vorst
Encyclopedia
Hendrik "Henk" Albertus van der Vorst (born on May 5, 1944) is a Dutch
mathematician
and Emeritus Professor of Numerical Analysis
at Utrecht University
. According to the Institute for Scientific Information
(ISI), his paper
on the Bi-CGSTAB method was the most cited
paper in the field of mathematics in the 1990s.
He is a member of the Royal Netherlands Academy of Arts and Sciences
(KNAW)
and the Netherlands Academy of Technology and Innovation.
In 2006 he was awarded a knighthood of the Order of the Netherlands Lion.
Henk van der Vorst is a Fellow of Society for Industrial and Applied Mathematics
(SIAM).
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,
the Bi-CGSTAB and (together with Kees Vuik) GMRESR
Krylov subspace
methods and (together with Gerard Sleijpen) the Jacobi-Davidson method
for solving ordinary, generalized, and nonlinear eigenproblems
.
He has analyzed convergence behavior of the conjugate gradient
and Lanczos
methods. He has also developed a number of preconditioner
s for parallel computers, 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
and one of the authors of the Templates projects for linear problems
and eigenproblems.
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and Emeritus Professor of Numerical Analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
at Utrecht University
Utrecht University
Utrecht University is a university in Utrecht, Netherlands. It is one of the oldest universities in the Netherlands and one of the largest in Europe. Established March 26, 1636, it had an enrollment of 29,082 students in 2008, and employed 8,614 faculty and staff, 570 of which are full professors....
. According to the Institute for Scientific Information
Institute for Scientific Information
The Institute for Scientific Information was founded by Eugene Garfield in 1960. It was acquired by Thomson Scientific & Healthcare in 1992, became known as Thomson ISI and now is part of the Healthcare & Science business of the multi-billion dollar Thomson Reuters Corporation.ISI offered...
(ISI), his paper
on the Bi-CGSTAB method was the most cited
ISI highly cited researcher
ISI Highly Cited is a database of "highly cited researchers"—scientific researchers whose publications are most often cited in academic journals over the past decade, published by the Institute for Scientific Information...
paper in the field of mathematics in the 1990s.
He is a member of the Royal Netherlands Academy of Arts and Sciences
Royal Netherlands Academy of Arts and Sciences
The Royal Netherlands Academy of Arts and Sciences is an organisation dedicated to the advancement of science and literature in the Netherlands...
(KNAW)
and the Netherlands Academy of Technology and Innovation.
In 2006 he was awarded a knighthood of the Order of the Netherlands Lion.
Henk van der Vorst is a Fellow of Society for Industrial and Applied Mathematics
Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics was founded by a small group of mathematicians from academia and industry who met in Philadelphia in 1951 to start an organization whose members would meet periodically to exchange ideas about the uses of mathematics in industry. This meeting led...
(SIAM).
His major contributions include preconditioned
Preconditioner
In mathematics, preconditioning is a procedure of an application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solution. Preconditioning is typically related to reducing a condition number of the problem...
iterative methods, in particular the ICCG (incomplete
Cholesky conjugate gradient) method (developed together with Koos Meijerink), a version of preconditioned conjugate gradient method,
the Bi-CGSTAB and (together with Kees Vuik) GMRESR
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,...
methods and (together with Gerard Sleijpen) the Jacobi-Davidson method
for solving ordinary, generalized, and nonlinear eigenproblems
Eigenvalue, eigenvector and eigenspace
The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain parallel to the original vector. For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix...
.
He has analyzed convergence behavior of the conjugate gradient
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 symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too...
and Lanczos
Lanczos algorithm
The Lanczos algorithm is an iterative algorithm invented by Cornelius Lanczos that is an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix or the singular value decomposition of a rectangular matrix. It is particularly useful for finding decompositions of very...
methods. He has also developed a number of preconditioner
Preconditioner
In mathematics, preconditioning is a procedure of an application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solution. Preconditioning is typically related to reducing a condition number of the problem...
s for parallel computers, 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
and one of the authors of the Templates projects for linear problems
and eigenproblems.
External links
- Home page of Henk van der Vorst at Utrecht University (Accessed December 2009)
- Private homepage of Henk van der Vorst (Accessed December 2009)