mathematics

Marlis Hochbruck

Marlis Hochbruck 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 Marlis Hochbruck rather than just read about it. In short: Marlis Hochbruck (born 12 June 1964) is a German applied mathematician and numerical analyst known for her research on matrix exponentials, exponential integrators, and their applications to the numerical solution of differential equations. She is a professor in the Institute for Applied and Numerical Mathematics at the Karlsruhe Institute of Technology.

Key takeaways

Marlis Hochbruck belongs to mathematics; place it in that map before memorising details.
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Reproduce the core statement of Marlis Hochbruck from memory before moving on to harder problems.

Reference excerpt

Marlis Hochbruck (born 12 June 1964) is a German applied mathematician and numerical analyst known for her research on matrix exponentials, exponential integrators, and their applications to the numerical solution of differential equations. She is a professor in the Institute for Applied and Numerical Mathematics at the Karlsruhe Institute of Technology.

Education and career Hochbruck went to high school in Krefeld, and studied Technomathematics at the Karlsruhe Institute of Technology from 1983 to 1989. She completed her Ph.D. at Karlsruhe in 1992. Her dissertation, Lanczos und Krylov-Verfahren für nicht-Hermitesche lineare Systeme, was jointly supervised by Wilhelm Niethammer and Michael Eiermann. After postdoctoral research at ETH Zurich, she became an assistant at the University of Würzburg in 1992, and moved to the University of Tübingen in 1994. She obtained her first professorship in 1998, in applied mathematics at the University of Düsseldorf, declining two offers of professorships at other German universities in the same year. In 2010 she returned to Karlsruhe as a professor. As well as holding her professorship at Karlsruhe, she has been a vice president of the Deutsche Forschungsgemeinschaft since 2014.

Selected publications Hochbruck, Marlis; Lubich, Christian (1997), "On Krylov subspace approximations to the matrix exponential operator", SIAM Journal on Numerical Analysis, 34 (5): 1911–1925, Bibcode:1997SJNA...34.1911H, CiteSeerX 10.1.1.452.3700, doi:10.1137/S0036142995280572, MR 1472203 {{citation}}: Cite uses deprecated parameter |citeseerx= (help) Hochbruck, Marlis; Lubich, Christian; Selhofer, Hubert (1998), "Exponential integrators for large systems of differential equations", SIAM Journal on Scientific Computing, 19 (5): 1552–1574, Bibcode:1998SJSC...19.1552H, doi:10.1137/S1064827595295337, MR 1618808 Hochbruck, Marlis; Ostermann, Alexander (2005), "Explicit exponential Runge–Kutta methods for semilinear parabolic problems", SIAM Journal on Numerical Analysis, 43 (3): 1069–1090, doi:10.1137/040611434, MR 2177796 Hochbruck, Marlis; Ostermann, Alexander (2010), "Exponential integrators", Acta Numerica, 19: 209–286, Bibcode:2010AcNum..19..209H, doi:10.1017/S0962492910000048, MR 2652783

References

External links Interview with Hochbruck in Forschung magazine (in German)

Illustrations

Worked examples

Example 1 — a first encounter with Marlis Hochbruck

Start with the simplest possible case. Write down what Marlis Hochbruck 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 Marlis Hochbruck 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 Marlis Hochbruck 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 Marlis Hochbruck

In research: Marlis Hochbruck 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 Marlis Hochbruck 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: Marlis Hochbruck is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1964 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Marlis Hochbruck 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 Marlis Hochbruck in 20 minutes

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Close the page and write down what Marlis Hochbruck means in your own words.
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Frequently asked questions

What is Marlis Hochbruck in simple terms?

Why does Marlis Hochbruck 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 Marlis Hochbruck?

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 Marlis Hochbruck.