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Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition how many elements need to be zero for a matrix to be considered sparse but a common criterion is that the number of non-zero elements is roughly the number of rows or columns. By contrast, if most of the elements are nonzero, then the matrix is considered dense. The number of zero-valued elements divided by the total number of elements is sometimes referred to as the sparsity of the matrix.
Jack J. Dongarra ForMemRS; is an 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 Texas A&M University's institute for advanced study (2014–2018). Dongarra is the founding director of Innovative Computing Laboratory.
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the routines have bindings for both C and Fortran. Although the BLAS specification is general, BLAS implementations are often optimized for speed on a particular machine, so using them can bring substantial performance benefits. BLAS implementations will take advantage of special floating point hardware such as vector registers or SIMD instructions.
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.
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.
The SIAM Journal on Scientific Computing (SISC), formerly SIAM Journal on Scientific & Statistical Computing, is a scientific journal focusing on the research articles on numerical methods and techniques for scientific computation. It is published by the Society for Industrial and Applied Mathematics (SIAM). Jan S. Hesthaven is the current editor-in-chief, assuming the role in January 2016. The impact factor is currently around 2.
The Sidney Fernbach Award established in 1992 by the IEEE Computer Society, in memory of Sidney Fernbach, one of the pioneers in the development and application of high performance computers for the solution of large computational problems as the Division Chief for the Computation Division at Lawrence Livermore Laboratory from the late 1950s through the 1970s. A certificate and $2,000 are awarded for outstanding contributions in the application of high performance computers using innovative approaches. The nomination deadline is 1 July each year.
Yousef Saad is an I.T. Distinguished Professor of Computer Science in the Department of Computer Science and Engineering at the University of Minnesota. He holds the William Norris Chair for Large-Scale Computing since January 2006. He is known for his contributions to the matrix computations, including the iterative methods for solving large sparse linear algebraic systems, eigenvalue problems, and parallel computing. Saad is listed as an ISI highly cited researcher in mathematics and is the author of the highly cited book Iterative Methods for Sparse Linear Systems. Yousef Saad is a SIAM fellow and a fellow of the AAAS (2011).
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.
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.
Alan Stuart Edelman is an American mathematician and computer scientist. He is a Professor of Applied Mathematics at the Massachusetts Institute of Technology and a Principal Investigator at the MIT Computer Science and AI Laboratory (CSAIL) where he leads a group in Applied Computing. In 2004 Professor Edelman founded Interactive Supercomputing, acquired by Microsoft.
Joel Aaron Tropp is the Steele Family Professor of Applied and Computational Mathematics in the Computing and Mathematical Sciences Department at the California Institute of Technology. He is known for work on sparse approximation, numerical linear algebra, and random matrix theory.
Communication-avoiding algorithms minimize movement of data within a memory hierarchy for improving its running-time and energy consumption. These minimize the total of two costs : arithmetic and communication. Communication, in this context refers to moving data, either between levels of memory or between multiple processors over a network. It is much more expensive than arithmetic.
bitpit is an open source modular library for scientific computing. The goal of bitpit is to ease the burden of writing scientific programs providing the common building blocks needed by every scientific application.
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.
Beresford Neill Parlett is an applied mathematician, specializing in numerical analysis and scientific computation.
References
- 1 2 3 Short bio, INRIA, retrieved 2020-06-12
- ↑ "Members of the team", Alpines: Algorithms and parallel tools for integrated numerical simulations, retrieved 2020-06-12
- ↑ Laura Grigori at the Mathematics Genealogy Project
- ↑ "Meet SIAM's Newest Leadership". SIAM News. Retrieved 2020-12-15.
- ↑ SIAM Activity Group on Supercomputing Best Paper Prize, Society for Industrial and Applied Mathematics, retrieved 2020-06-12
- ↑ "SIAM Announces Class of 2020 Fellows", SIAM News, SIAM, 31 March 2020, retrieved 2020-06-12
