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.
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming.
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
James Hardy Wilkinson FRS was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering.
Multi-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. It is also known as multidisciplinary system design optimization (MSDO), and Multidisciplinary Design Analysis and Optimization (MDAO).
Jack Joseph Dongarra is an American computer scientist and mathematician. He is the American University Distinguished Professor of Computer Science in the Electrical Engineering and Computer Science Department at the University of Tennessee. He holds the position of a Distinguished Research Staff member in the Computer Science and Mathematics Division at Oak Ridge National Laboratory, Turing Fellowship in the School of Mathematics at the University of Manchester, and is an adjunct professor in the Computer Science Department at Rice University. He served as a faculty fellow at the Texas A&M University Institute for Advanced Study (2014–2018). Dongarra is the founding director of the Innovative Computing Laboratory at the University of Tennessee. He was the recipient of the Turing Award in 2021.
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems. It is an area of science that spans many disciplines, but at its core, it involves the development of models and simulations to understand natural systems.
Cornelius (Cornel) Lanczos was a Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians.
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.
Stanley Osher is an American mathematician, known for his many contributions in shock capturing, level-set methods, and PDE-based methods in computer vision and image processing. Osher is a professor at the University of California, Los Angeles (UCLA), Director of Special Projects in the Institute for Pure and Applied Mathematics (IPAM) and member of the California NanoSystems Institute (CNSI) at UCLA.
James Albert Sethian is a professor of mathematics at the University of California, Berkeley and the head of the Mathematics Group at the United States Department of Energy's Lawrence Berkeley National Laboratory.
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible.
Max D. Gunzburger, Francis Eppes Distinguished Professor of Mathematics at Florida State University, is an American mathematician and computational scientist affiliated with the Florida State interdisciplinary Department of Scientific Computing. He was the 2008 winner of the SIAM W.T. and Idalia Reid Prize in Mathematics. His seminal research contributions include flow control, finite element analysis, superconductivity and Voronoi tessellations. He has also made contributions in the areas of aerodynamics, materials, acoustics, climate change, groundwater, image processing and risk assessment.
Magnus Rudolph Hestenes was an American mathematician best known for his contributions to calculus of variations and optimal control. As a pioneer in computer science, he devised the conjugate gradient method, published jointly with Eduard Stiefel.
Philippe G. Ciarlet is a French mathematician, known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates and shells and differential geometry.
Bruce Howard McCormick (1928–2007) was an American computer scientist, Emeritus Professor at the Department of Computer Science, and founding director of the Brain Networks Lab at Texas A&M University.
Yurii Nesterov is a Russian mathematician, an internationally recognized expert in convex optimization, especially in the development of efficient algorithms and numerical optimization analysis. He is currently a professor at the University of Louvain (UCLouvain).
Marvin Stein (1924-2015) was a mathematician and computer scientist, and the "father of computer science" at the University of Minnesota.
Berthold Klaus Paul Horn is an American scientist working in the field of artificial intelligence and computer vision. He is Professor of Electrical Engineering and Computer Science at Massachusetts Institute of Technology (MIT). He is also Principal Investigator at the Computer Science and Artificial Intelligence Laboratory (CSAIL) at MIT.
Roland Andrew Sweet was an American mathematician and computer scientist.
