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SLATEC
SLATEC Common Mathematical Library is a FORTRAN 77 library of over 1400 general purpose mathematical and statistical routines. The code was developed at US Government research laboratories and is therefore public domain software. "SLATEC" is an acronym for the Sandia, Los Alamos, Air Force Weapons Laboratory Technical Exchange Committee, an organization formed in 1974 to foster the exchange of technical information between the computer centers of three US government laboratories. Project history and current status In 1977, the SLATEC Common Mathematical Library (CML) Subcommittee decided to construct a library of FORTRAN subprograms to provide portable, non-proprietary, mathematical software that could be used on a variety of computers, including supercomputers, at the three sites. The computers centers of the Lawrence Livermore National Laboratory, the National Bureau of Standards and the Oak Ridge National Laboratory also participated from 1980–81 onwards. The main ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
QUADPACK
QUADPACK is a FORTRAN 77 library for numerical integration of one-dimensional functions. It was included in the SLATEC Common Mathematical Library and is therefore in the public domain. The individual subprograms are also available on netlib. The GNU Scientific Library reimplemented the QUADPACK routines in C. SciPy provides a Python interface to part of QUADPACK. Routines The main focus of QUADPACK is on ''automatic'' integration routines in which the user inputs the problem and an absolute or relative error tolerance and the routine attempts to perform the integration with an error no larger than that requested. There are nine such automatic routines in QUADPACK, in addition to a number of non-automatic routines. All but one of the automatic routines use adaptive quadrature. Each of the adaptive routines also have versions suffixed by E that have an extended parameter list that provides more information and allows more control. Double precision versions of all routines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Netlib
Netlib is a repository of software for scientific computing maintained by AT&T, Bell Laboratories, the University of Tennessee and Oak Ridge National Laboratory. Netlib comprises many separate programs and libraries. Most of the code is written in C and Fortran, with some programs in other languages. History The project began with email distribution on UUCP, ARPANET and CSNET in the 1980s. The code base of Netlib was written at a time when computer software was not yet considered merchandise. Therefore, no license terms or terms of use are stated for many programs. Before the Berne Convention Implementation Act of 1988 (and the earlier Copyright Act of 1976) works without an explicit copyright notice were public-domain software. Also, most of the Netlib code is work of US government employees and therefore in the public domain. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FFTPACK
FFTPACK is a package of Fortran subroutines for the fast Fourier transform. It includes complex, real, sine, cosine, and quarter-wave transforms. It was developed by Paul Swarztrauber of the National Center for Atmospheric Research, and is included in the general-purpose mathematical library SLATEC. Much of the package is also available in C and Java translations. See also * FFTW * LAPACK LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It al ... References * * * Computer libraries FFT algorithms Public-domain software with source code {{compu-library-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sandia National Laboratories
Sandia National Laboratories (SNL), also known as Sandia, is one of three research and development laboratories of the United States Department of Energy's National Nuclear Security Administration (NNSA). Headquartered in Kirtland Air Force Base in Albuquerque, New Mexico, it has a second principal facility next to Lawrence Livermore National Laboratory in California and a test facility in Waimea, Kauai, Hawaii. Sandia is owned by the U.S. federal government but privately managed and operated by National Technology and Engineering Solutions of Sandia, a wholly owned subsidiary of Honeywell International. Established in 1949, SNL is a "multimission laboratory" with the primary goal of advancing U.S. national security by developing various science-based technologies. Its work spans roughly 70 areas of activity, including nuclear deterrence, arms control, nonproliferation, hazardous waste disposal, and climate change. Sandia hosts a wide variety of research initiatives, inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guide To Available Mathematical Software
The Guide to Available Mathematical Software (GAMS) is a project of the National Institute of Standards and Technology to classify mathematical software by the type of problem that it solves. GAMS became public in 1985. It indexes Netlib and other packages, some of them public domain software and some proprietary software Proprietary software is computer software, software that is deemed within the free and open-source software to be non-free because its creator, publisher, or other rightsholder or rightsholder partner exercises a legal monopoly afforded by modern .... References External links Guide to Available Mathematical Software''(GAMS project home page.)'' Mathematical software Public-domain software with source code {{mathpublication-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Association For Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional membership group, claiming nearly 110,000 student and professional members . Its headquarters are in New York City. The ACM is an umbrella organization for academic and scholarly interests in computer science ( informatics). Its motto is "Advancing Computing as a Science & Profession". History In 1947, a notice was sent to various people: On January 10, 1947, at the Symposium on Large-Scale Digital Calculating Machinery at the Harvard computation Laboratory, Professor Samuel H. Caldwell of Massachusetts Institute of Technology spoke of the need for an association of those interested in computing machinery, and of the need for communication between them. ..After making some inquiries during May and June, we believe there is ample interest to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparse Matrix
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 regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Function
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the List of mathematical functions contains functions that are commonly accepted as special. Tables of special functions Many special functions appear as solutions of differential equations or integrals of elementary functions. Therefore, tables of integrals usually include descriptions of special functions, and tables of special functions include most important integrals; at least, the integral representation of special functions. Because symmetries of differential equations are essential to both physics and mathematics, the theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics. Sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Reduction
Cyclic reduction is a numerical method for solving large linear systems by repeatedly splitting the problem. Each step eliminates even or odd rows and columns of a matrix and remains in a similar form. The elimination step is relatively expensive but splitting the problem allows parallel computation. Applicability The method only applies to matrices that can be represented as a (block) Toeplitz matrix, such problems often arise in implicit solutions for partial differential equations on a lattice. For example fast solvers for Poisson's equation express the problem as solving a tridiagonal matrix, discretising the solution on a regular grid. Accuracy Systems which have good numerical stability initially tend to get better with each step to a point where a good approximate solution can be given, but because the special matrix form must be preserved pivoting cannot be performed to improve numerical accuracy. Comparison to multigrid The method is not iterative, it seeks an exact sol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O\left(N^2\right), which arises if one simply applies the definition of DFT, to O(N \log N), where N is the data size. The difference in speed can be enormous, especially for long data sets where ''N'' may be in the thousands or millions. In the presence of round-off error, many FFT algorith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvector
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
