In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method. Arnoldi finds an approximation to the eigenvalues and eigenvectors of general matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.
In linear algebra, the order-rKrylov 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,
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.
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
David M. Young Jr. was an American mathematician and computer scientist who was one of the pioneers in the field of modern numerical analysis/scientific computing.
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.
Peter Wynn (1931—2017) was an English mathematician. His main achievements concern approximation theory – in particular the theory of Padé approximants – and its application in numerical methods for improving the rate of convergence of sequences of real numbers.
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.
Rajendra Bhatia is an Indian mathematician, author, and educator. He is currently a professor of mathematics at Ashoka University located in Sonipat, Haryana ,India.
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling.
Valeria Simoncini is an Italian researcher in numerical analysis who works as a professor in the mathematics department at the University of Bologna. Her research involves the computational solution of equations involving large matrices, and their applications in scientific computing. She is the chair of the SIAM Activity Group on Linear Algebra.
Edmond Chow is an associate professor in the School of Computational Science and Engineering of Georgia Institute of Technology. His main areas of research are in designing numerical methods for high-performance computing and applying these methods to solve large-scale scientific computing problems.
Robert James Plemmons is an American mathematician specializing in computational mathematics. He is the Emeritus Z. Smith Reynolds Professor of Mathematics and Computer Science at Wake Forest University. In 1979, Plemmons co-authored the book Nonnegative Matrices in the Mathematical Sciences.
Marlis Hochbruck 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.
Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation.
The International Linear Algebra Society (ILAS) is a professional mathematical society organized to promote research and education in linear algebra, matrix theory and matrix computation. It serves the international community through conferences, publications, prizes and lectures. Membership in ILAS is open to all mathematicians and scientists interested in furthering its aims and participating in its activities.
Daniel Kressner is a German numerical analyst. He has a Chair of Numerical Algorithms and High Performance Computing in the Institute of Mathematics at EPF Lausanne.
Stefan Dietrich Güttel is a German numerical analyst. He is Professor of Applied Mathematics in the Department of Mathematics at the University of Manchester.
