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 like economics, 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.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Heinz-Otto Kreiss was a German mathematician in the fields of numerical analysis, applied mathematics, and what was the new area of computing in the early 1960s. Born in Hamburg, Germany, he earned his Ph.D. at Kungliga Tekniska Högskolan in 1959. Over the course of his long career, Kreiss wrote a number of books in addition to the purely academic journal articles he authored across several disciplines. He was professor at Uppsala University, California Institute of Technology and University of California, Los Angeles (UCLA). He was also a member of the Royal Swedish Academy of Sciences. At the time of his death, Kreiss was a Swedish citizen, living in Stockholm. He died in Stockholm in 2015, aged 85.
Lloyd Nicholas Trefethen is an American mathematician, professor of numerical analysis and until 2023 head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford.
Hans F. Weinberger was an Austrian-American mathematician, known for his contributions to variational methods for eigenvalue problems, partial differential equations, and fluid dynamics.
Chi-Wang Shu is the Theodore B. Stowell University Professor of Applied Mathematics at Brown University. He is known for his research in the fields of computational fluid dynamics, numerical solutions of conservation laws and Hamilton–Jacobi type equations. Shu has been listed as an ISI Highly Cited Author in Mathematics by the ISI Web of Knowledge.
Helge Holden is a Norwegian mathematician working in the field of differential equations and mathematical physics. He was Praeses of the Royal Norwegian Society of Sciences and Letters from 2014 to 2016.
In numerical analysis and applied mathematics, sinc numerical methods are numerical techniques for finding approximate solutions of partial differential equations and integral equations based on the translates of sinc function and Cardinal function C(f,h) which is an expansion of f defined by
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).
Burton Wendroff is an American applied mathematician known for his contributions to the development of numerical methods for the solution of hyperbolic partial differential equations. The Lax–Wendroff method for the solution of hyperbolic PDE is named for Wendroff.
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.
Arieh Iserles is a computational mathematician, currently Professor of the Numerical Analysis of Differential Equations at the University of Cambridge and a member of the Department of Applied Mathematics and Theoretical Physics.
Irena Lasiecka is a Polish-American mathematician, a Distinguished University Professor of mathematics and chair of the mathematics department at the University of Memphis. She is also co-editor-in-chief of two academic journals, Applied Mathematics & Optimization and Evolution Equations & Control Theory.
Björn Sandstede is a German applied mathematician. He is currently the Alumni-Alumnae University Professor of Applied Mathematics at Brown University, where he serves as chair of the department.
Weizhu Bao is a Chinese mathematician at the National University of Singapore (NUS). He is known for his work in applied mathematics with applications in quantum physics and chemistry and materials science, especially Bose-Einstein condensation (BEC) and highly oscillatory partial differential equations.
Panagiotis E. Souganidis is an American mathematician, specializing in partial differential equations.
Angela Kunoth is a German mathematician specializing in the numerical analysis of partial differential equations. She is a professor of mathematics at the University of Cologne, and the editor-in-chief of SIAM Journal on Numerical Analysis.
Charles Anthony Micchelli is an American mathematician, with an international reputation in numerical analysis, approximation theory, and machine learning.
Albert Cohen is a French mathematician, specializing in approximation theory, numerical analysis, and digital signal processing.
David James Silvester is a British numerical analyst. He has a Chair in Numerical Analysis and is the Head of Applied Mathematics in the Department of Mathematics at the University of Manchester.
