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 at finding 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.
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics.
In electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related k-means clustering algorithm, it repeatedly finds the centroid of each set in the partition and then re-partitions the input according to which of these centroids is closest. In this setting, the mean operation is an integral over a region of space, and the nearest centroid operation results in Voronoi diagrams.
George J. Fix was an American mathematician who collaborated on several seminal papers and books in the field of finite element method. In addition to his work in mathematics, Fix was a beer and homebrewing enthusiast and educator, as well as the author of several books about brewing. He died of cancer in 2002.
In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation in which the generating point of each Voronoi cell is also its centroid. It can be viewed as an optimal partition corresponding to an optimal distribution of generators. A number of algorithms can be used to generate centroidal Voronoi tessellations, including Lloyd's algorithm for K-means clustering or Quasi-Newton methods like BFGS.
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.
Mohammed Yousuff Hussaini is an Indian born American applied mathematician. He is the Sir James Lighthill Professor of Mathematics and Computational Science & Engineering at the Florida State University, United States. Hussaini is also the holder of the TMC Eminent Scholar Chair in High Performance Computing at FSU. He is widely known for his research in scientific computation, particularly in the field of computational fluid dynamics (CFD) and Control and optimization. Hussaini co-authored the popular book Spectral Methods in Fluid Dynamics with Claudio Canuto, Alfio Quarteroni, and Thomas Zang. He is the editor-in-chief of the journal Theoretical and Computational Fluid Dynamics.
Jinchao Xu is an American-Chinese mathematician. He is currently the Verne M. Willaman Professor in the Department of Mathematics at the Pennsylvania State University, University Park. He is known for his work on multigrid methods, domain decomposition methods, finite element methods, and more recently deep neural networks.
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).
Mary Fanett Wheeler is an American mathematician. She is known for her work on numerical methods for partial differential equations, including domain decomposition methods.
Qiang Du, the Fu Foundation Professor of Applied Mathematics at Columbia University, is a Chinese mathematician and computational scientist. Prior to moving to Columbia, he was the Verne M. Willaman Professor of Mathematics at Pennsylvania State University affiliated with the Pennsylvania State University Department of Mathematics and Materials Sciences.
James Weldon Demmel Jr. is an American mathematician and computer scientist, the Dr. Richard Carl Dehmel Distinguished Professor of Mathematics and Computer Science at the University of California, Berkeley.
Marsha J. Berger is an American computer scientist. Her areas of research include numerical analysis, computational fluid dynamics, and high-performance parallel computing. She is a Silver Professor (emeritus) of Computer Science and Mathematics in the Courant Institute of Mathematical Sciences of New York University. She is Group Leader of Modeling and Simulation in the Center for Computational Mathematics at the Flatiron Institute.
Thomas Yizhao Hou is the Charles Lee Powell Professor of Applied and Computational Mathematics in the Department of Computing and Mathematical Sciences at the California Institute of Technology. He is known for his work in numerical analysis and mathematical analysis.
Hans Petter Langtangen was a Norwegian scientist trained in mechanics and scientific computing. Langtangen was the director of the Centre for Biomedical Computing, a Norwegian Center of Excellence hosted by Simula Research Laboratory. He was a professor of scientific computing at the University of Oslo, and was editor-in-chief of SIAM Journal on Scientific Computing 2011–2015.
Lexing Ying is a professor of mathematics at Stanford University, where he is also a member of the Institute for Computational and Mathematical Engineering. He specializes in scientific computing and numerical analysis. In particular, his research concerns the design of numerical algorithms for problems in scientific computing.
Tang Tao is a Chinese mathematician currently serving as President of BNU-HKBU United International College. Tang is a member of the Chinese Academy of Sciences. He is a fellow of the Society for Industrial and Applied Mathematics and American Mathematical Society.
Maria Emelianenko is a Russian-American applied mathematician and materials scientist known for her work in numerical algorithms, scientific computing, grain growth, and centroidal Voronoi tessellations. She is a professor of mathematical sciences at George Mason University.
Assyr Abdulle was a Swiss mathematician. He specialized in numerical mathematics.
Karl Kunisch is an Austrian mathematician.
United States 