mathematics

Henk van der Vorst

Henk van der Vorst is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Henk van der Vorst rather than just read about it. In short: Hendrik "Henk" Albertus van der Vorst (born 5 May 1944, Venlo) 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 BiCGSTAB method was the most cited paper in the field of mathematics in the 1990s.

Key takeaways

Henk van der Vorst belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Henk van der Vorst to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Henk van der Vorst from memory before moving on to harder problems.

Reference excerpt

Hendrik "Henk" Albertus van der Vorst (born 5 May 1944, Venlo) 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 BiCGSTAB 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) since 2002 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 BiCGSTAB 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 preconditioners 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 Iterative Krylov Methods for Large Linear systems and one of the authors of the Templates projects for linear problems and eigenproblems.

References

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) Henk van der Vorst at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Henk van der Vorst

Start with the simplest possible case. Write down what Henk van der Vorst claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Henk van der Vorst before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Henk van der Vorst ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Henk van der Vorst

In research: Henk van der Vorst appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Henk van der Vorst in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Henk van der Vorst is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century Dutch mathematicians, 21st-century Dutch mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henk van der Vorst outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Henk van der Vorst in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henk van der Vorst means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Henk van der Vorst out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Henk van der Vorst in simple terms?

Why does Henk van der Vorst matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Henk van der Vorst?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Henk van der Vorst.