Marlis Hochbruck (born 12 June 1964) [1] 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. [2]
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. [1] Her dissertation, Lanczos und Krylov-Verfahren für nicht-Hermitesche lineare Systeme, was jointly supervised by Wilhelm Niethammer and Michael Eiermann. [3]
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. [1]
As well as holding her professorship at Karlsruhe, she has been a vice president of the Deutsche Forschungsgemeinschaft since 2014. [1]
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals.
Gene Howard Golub, was an American numerical analyst who taught at Stanford University as Fletcher Jones Professor of Computer Science and held a courtesy appointment in electrical engineering.
Lloyd Nicholas Trefethen is an American mathematician, professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford.
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control, and can be formulated to construct solutions in a memory-efficient, factored form. It is also used to numerically solve parabolic and elliptic partial differential equations, and is a classic method used for modeling heat conduction and solving the diffusion equation in two or more dimensions. It is an example of an operator splitting method.
Roger Meyer Temam is a French applied mathematician working in numerical analysis, nonlinear partial differential equations and fluid mechanics. He graduated from the University of Paris – the Sorbonne in 1967, completing a doctorate under the direction of Jacques-Louis Lions. He has published over 400 articles, as well as 12 books.
Randall J.. LeVeque is a Professor of Applied Mathematics at University of Washington who works in many fields including numerical analysis, computational fluid dynamics, and mathematical theory of conservation laws. Among other contributions, he is lead developer of the open source software project Clawpack for solving hyperbolic partial differential equations using the finite volume method. With Zhilin Li, he has also devised a numerical technique called the immersed interface method for solving problems with elastic boundaries or surface tension.
Richard Steven Varga was an American mathematician who specialized in numerical analysis and linear algebra. He was an Emeritus University Professor of Mathematical Sciences at Kent State University and an adjunct Professor at Case Western Reserve University. Varga was known for his contributions to many areas of mathematics, including matrix analysis, complex analysis, approximation theory, and scientific computation. He was the author of the classic textbook Matrix Iterative Analysis. Varga served as the Editor-in-Chief of the journal Electronic Transactions on Numerical Analysis (ETNA).
Andrew Knyazev is an American mathematician. He graduated from the Faculty of Computational Mathematics and Cybernetics of Moscow State University under the supervision of Evgenii Georgievich D'yakonov in 1981 and obtained his PhD in Numerical Mathematics at the Russian Academy of Sciences under the supervision of Vyacheslav Ivanovich Lebedev in 1985. He worked at the Kurchatov Institute between 1981–1983, and then to 1992 at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, headed by Gury Marchuk.
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
Exponential integrators are a class of numerical methods for the solution of ordinary differential equations, specifically initial value problems. This large class of methods from numerical analysis is based on the exact integration of the linear part of the initial value problem. Because the linear part is integrated exactly, this can help to mitigate the stiffness of a differential equation. Exponential integrators can be constructed to be explicit or implicit for numerical ordinary differential equations or serve as the time integrator for numerical partial differential equations.
Sara Zahedi is an Iranian-Swedish mathematician who works in computational fluid dynamics and holds an associate professorship in numerical analysis at the Royal Institute of Technology (KTH) in Sweden. She is one of ten winners and the only female winner of the European Mathematical Society Prize for 2016 "for her outstanding research regarding the development and analysis of numerical algorithms for partial differential equations with a focus on applications to problems with dynamically changing geometry". The topic of Zahedi's EMS Prize lecture was her recent research on the CutFEM method of solving fluid dynamics problems with changing boundary geometry, such as arise when simulating the dynamics of systems of two immiscible liquids. This method combines level set methods to represent the domain boundaries as cuts through an underlying uniform grid, together with numerical simulation techniques that can adapt to the complex geometries of grid cells cut by these boundaries.
Heike Fassbender is a German mathematician specializing in numerical linear algebra. She is a professor in the Institute for Computational Mathematics at the Technical University of Braunschweig, and the president for the 2017–2019 term of the Gesellschaft für Angewandte Mathematik und Mechanik.
Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation.
Christian Lubich is an Austrian mathematician, specializing in numerical analysis.
Gerhard Wanner is an Austrian mathematician.
Charles William Clenshaw was an English mathematician, specializing in numerical analysis. He is known for the Clenshaw algorithm (1955) and Clenshaw–Curtis quadrature (1960). In a 1984 paper Beyond Floating Point, Clenshaw and Frank W. J. Olver introduced symmetric level-index arithmetic.
Karl Kunisch is an Austrian mathematician.
Stefan Dietrich Güttel is a German numerical analyst. He is Professor of Applied Mathematics in the Department of Mathematics at the University of Manchester.
Daniel B. Szyld is an Argentinian and American mathematician who is a professor at Temple University in Philadelphia. He has made contributions to numerical and applied linear algebra as well as matrix theory.
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