|
Foundations Of Computational Mathematics
Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications. Aim FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to: *Approximation Theory *Computational Algebraic Geometry *Computational Dynamics *Computational Harmonic Analysis, Image, and Signal Processing *Computational Number Theory *Computational Topology and Geometry *Continuous Optimization * Foundations of Numerical PDE's * Geometric Integration and Computational Mechanics *Graph Theory and Combinatorics * Information-based Complexi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfgang Dahmen (mathematician)
Wolfgang Dahmen (born 19 October 1949) is a German mathematician working in approximation theory, numerical analysis, and partial differential equations. In 2002 he was awarded the Gottfried Wilhelm Leibniz Prize and in 2011 the Gauss Lectureship. He was also a taekwondo athlete. He has been the Chair of the Society for the Foundations of Computational Mathematics (2014–). In 2019 he was named a SIAM Fellow "for contributions to numerical methods for partial differential equations, signal processing, and learning". References Further readingMultiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of His 60th Birthday Ronald DeVore, Angela Kunoth Angela Kunoth (born 22 June 1963) 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 Nu ..., Springer, 2009, Homepage at Institut fü ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Linear Algebra
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. Numerical linear algebra aims to solve problems of continuous mathematics using finite precision computers, so its applications to the natural and social scienc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Sciences Research Institute
The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, California. It is widely regarded as a world leading mathematical center for collaborative research, drawing thousands of leading researchers from around the world each year. The institute was founded in 1982, and its funding sources include the National Science Foundation, private foundations, corporations, and more than 90 universities and institutions. The institute is located at 17 Gauss Way on the Berkeley campus, close to Grizzly Peak in the Berkeley Hills. Because of its contribution to the nation's scientific potential, SLMath's activity is supported by the National Science Foundation and the National Security Agency. Private individuals, foundations, and nearly 100 Academic Sponsor Institutions, including the top mathematics depar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Palis
__NOTOC__ Jacob Palis Jr. (born 15 March 1940) is a Brazilian mathematician and professor. Palis' research interests are mainly dynamical systems and differential equations. Some themes are global stability and hyperbolicity, bifurcations, attractors and chaotic systems. Biography Jacob Palis was born in Uberaba, Minas Gerais. His father was a Lebanese immigrant, and his mother was a Syrian immigrant. The couple had eight children (five men and three women), and Jacob was the youngest. His father was a merchant, owner of a large store, and supported and funded the studies of his children. Palis said that he already enjoyed mathematics in his childhood.http://www.faperj.br/downloads/revista/Rio_Pesquisa_4_2008.pdf At 16, Palis moved to Rio de Janeiro to study engineering at the University of Brazil – now UFRJ. He was approved in first place in the entrance exam, but was not old enough to be accepted; he then had to take the university's entry exam again a year later, at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Renegar
James Milton Renegar Jr. (born May 14, 1955) is an American mathematician, specializing in optimization algorithms for linear programming and nonlinear programming. Biography In 1983 he received his Ph.D. in mathematics from the University of California, Berkeley. His Ph.D. thesis ''On the Computational Complexity of Simplicial Algorithms in Approximation Zeros of Complex Polynomials'' was supervised by Stephen Smale. After postdoc positions, Renegar joined in 1987 the faculty of the School of Operations Research and Information Engineering at Cornell University and is now a full professor there. Renegar is a leading expert on optimization algorithms. In recent years, the focus of his research is devising new algorithms for linear programming. He has done research on 'interior-point methods for convex optimization (for which he wrote a well-known introductory monograph), quantifier elimination methods for the first-order theory of the reals, development of the notion of " conditi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Narendra Karmarkar
Narendra Krishna Karmarkar (born Circa 1956) is an Indian Mathematician. Karmarkar developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher. He invented one of the first provably polynomial time algorithms for linear programming, which is generally referred to as an interior point method. The algorithm is a cornerstone in the field of Linear Programming. He published his famous result in 1984 while he was working for Bell Laboratories in New Jersey. Biography Karmarkar received his B.Tech in Electrical Engineering from IIT Bombay in 1978, MS from the California Institute of Technology in 1979, and PhD in Computer Science from the University of California, Berkeley in 1983 under the supervision of Richard M. Karp. Karmarkar was a post-doctoral research fellow at IBM research (1983), Member of Technical Staff and fellow at Mathematical Sciences Research Center, AT&T Bell Laboratories (1983-1998), professor of mathematics at M.I.T. (1991), at Institute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arieh Iserles
Arieh Iserles (born 2 September 1947) 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. He studied at the Hebrew University of Jerusalem and Ben-Gurion University of the Negev and wrote his PhD dissertation on numerical methods for stiff ordinary differential equations. His research comprises many themes in computational and applied mathematics: ordinary and partial differential equations, approximation theory, geometric numerical integration, orthogonal polynomials, functional equations, computational dynamics and the computation of highly oscillatory phenomena. He has written a textbook, ''A First Course in the Numerical Analysis of Differential Equations'' (Cambridge University Press, 2nd ed. 2009). Arieh Iserles is the Managing Editor of Acta Numerica, Editor-in-Chief of IMA Journal of Numerical Analysis and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felipe Cucker
Juan Felipe Cucker Farkas (born 1958) is an Uruguayan mathematician and theoretical computer scientist who has done research into the complexity theory of the Blum–Shub–Smale computational model and the complexity of numerical algorithms in linear programming and numerical algebraic geometry. Biography Cucker was born in Montevideo in 1958. Also: . Due to the situation in Uruguay in the 70s, he emigrated to Spain to study the bachelor of mathematics at the University of Barcelona, which he completed in 1983. He obtained his Ph.D. degree at the University of Cantabria and University of Rennes 1 in 1986 under the supervision Tomás Recio and Michel Coste. His thesis was about Nash functions on real algebraic varieties. From 1987 to 1992 Cucker was professor at the Polytechnic University of Catalonia. In 1992 Cucker became professor at the recently created Pompeu Fabra University. In 1995 he was promoted to chair professor at this university. In 1993 he organized the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Shub
Michael Ira Shub (born August 17, 1943) is an American mathematician who has done research into dynamical systems and the complexity of real number algorithms. Biography Shub obtained his Ph.D. degree at the University of California, Berkeley with a thesis entitled '' Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was Stephen Smale. From 1967 to 1985 he worked at Brandeis University, the University of California, Santa Cruz and the Queens College at the City University of New York. From 1985 to 2004 he joined IBM's Thomas J. Watson Research Center. From 2004 to 2010 he worked at the University of Toronto. After 2010 he is a researcher at the University of Buenos Aires and at the City University of New York. Shub was the Chair of the Society for the Foundations of Computational Mathematics from 1995 to 1997. In 2012, a conference, ''From Dynamics to Complexity'', was organised at the Fields Institute in Toronto celebrating his work. In 2015 he w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–1961 and 1964–1995), where he currently is Professor Emeritus, with research interests in algorithms, numerical analysis and global analysis. Education and career Smale was born in Flint, Michigan and entered the University of Michigan in 1948. Initially, he was a good student, placing into an honors calculus sequence taught by Bob Thrall and earning himself A's. However, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics. However, with some luck, Smale was accepted as a graduate student at the University of Michigan's mathematics department. Yet again, Smale performed poorly in his first years, earning a C average as a gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Computing
Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed by simple bit-wise operations on the streams. Stochastic computing is distinct from the study of randomized algorithms. Motivation and a simple example Suppose that p,q \in ,1/math> is given, and we wish to compute p \times q. Stochastic computing performs this operation using probability instead of arithmetic. Specifically, suppose that there are two random, independent bit streams called ''stochastic number''s (i.e. Bernoulli processes), where the probability of a one in the first stream is p, and the probability in the second stream is q. We can take the logical AND of the two streams. The probability of a one in the output stream is pq. By observing enough output bits and measuring the frequency of ones, it is possible to estimate pq to arbitrary accuracy. The operation above converts a fairly complicated computation ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special cases. The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by P. L. Chebyshev and was pursued by A. A. Markov and T. J. Stieltjes. They appear in a wide variety of fields: numerical analysis ( quadrature rules), probability theory, representation theory (of Lie groups, quantum groups, and related objects), enumerative combinatorics, algebraic combinatorics, mathematical physics (the theory of random matr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
