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Mansa Musa was the ruler of the Mali Empire in West Africa. Details recorded here should be sourced; unknown information is left blank.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
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The NAG Numerical Library is a commercial software product developed and sold by The Numerical Algorithms Group Ltd. It is a software library of numerical-analysis routines, containing more than 1,900 mathematical and statistical algorithms. Areas covered by the library include linear algebra, optimization, quadrature, the solution of ordinary and partial differential equations, regression analysis, and time series analysis.
Users of the NAG Library call its routines from within their applications to incorporate its mathematical or statistical functionality and to solve numerical problems - for example, finding the minimum or maximum of a function, fitting a curve or surface to data, or solving a differential equation. The NAG Library [1] can be accessed from a variety of programming languages and environments such as C/C++,[2] Fortran,[3]Python,[4] MATLAB,[5] Java,[6] and .NET.[7] A separate library supports Automatic differentiation (AD).[8] The main supported systems are currently Windows, Linux and macOS running on x86-64 architectures; 32-bit Windows support is being phased out. Some NAG mathematical optimization solvers are accessible via the optimization modelling suite.[9]
The original version of the NAG Library was written in ALGOL 60 and Fortran. It contained 98 user-callable routines, and was released for the International Computers Limited (ICL) 1906A and 1906S machines on October 1, 1971. Three further Marks of the library appeared in the following five years; during this time the ALGOL version was ported to ALGOL 68, with the following platforms being supported: CDC 7600/CYBER (CDC ALGOL 68), IBM 360/370/AMDAHL (FLACC ALGOL 68), ICL 1900 (ALGOL 68R), ICL 1906A/S (ALGOL 68R), ICL 2900 (ALGOL 68RS) and Telefunken TR440 (ALGOL 68C).
The first partially vectorized implementation of the NAG Fortran Library for the Cray-1 was released in 1983, while the first release of the NAG Parallel Library (which was specially designed for distributed memory parallel computer architectures) was in the early 1990s. Mark 1 of the NAG C Library was released in 1990. In 1992, the Library incorporated LAPACK routines for the first time; NAG had been a collaborator in the LAPACK project since 1987. The first release of the NAG Library for SMP & Multicore,[10] which takes advantage of the shared memory parallelism of Symmetric Multi-Processors (SMP) and multicore processors, appeared in 1997 for multiprocessor machines built using the Dec Alpha and SPARC architectures. The NAG Library for .NET, which is a CLI DLL assembly containing methods and objects that give Common Language Infrastructure (CLI) users access to NAG algorithms, was first released in 2010.
Mark 29 of the NAG Library includes mathematical and statistical algorithms organised into chapters.[11]
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
The NAG Numerical Library is a commercial software product developed and sold by The Numerical Algorithms Group Ltd. It is a software library of numerical-analysis routines, containing more than 1,900 mathematical and statistical algorithms. Areas covered by the library include linear algebra, optimization, quadrature, the solution of ordinary and partial differential equations, regression analysis, and time series analysis. Users of the NAG Library call its routines from within their applications to incorporate its mathematical or statistical functionality and to solve numerical problems - for example, finding the minimum or maximum of a function, fitting a curve or surface to data, or solving a differential equation. The NAG Library can be accessed from a variety of programming languages and environments such as C/C++, Fortran,Python, MATLAB, Java, and .NET. A separate library supports Automatic differentiation (AD). The main supported systems are currently Windows, Linux and macOS running on x86-64 architectures; 32-bit Windows support is being phased out. Some NAG mathematical optimization solvers are accessible via the optimization modelling suite.
This is a list of numerical libraries, which are libraries used in software development for performing numerical calculations. It is not a complete listing but is instead a list of numerical libraries with articles on Wikipedia, with few exceptions. The choice of a typical library depends on a range of requirements such as: desired features (e.g. large dimensional linear algebra, parallel computation, partial differential equations), licensing, readability of API, portability or platform/compiler dependence (e.g. Linux, Windows, Visual C++, GCC), performance, ease-of-use, continued support from developers, standard compliance/precision/reproducibility, specialized optimization in code for specific application scenario, or even the size of the code-base to be installed. This list is sorted by from what languages a library is designed to be usable, not by what the libraries are written in (an implementation detail). Some numerical tasks are performed by standard library functions. These are not listed here, though some "see also" links to relevant pages may be included.
Numerical analysis is the study of algorithms for the problems of continuous mathematics. These algorithms involve real or complex variables (in contrast to discrete mathematics), and typically use numerical approximation in addition to symbolic manipulation. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, 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 (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology. Before modern computers, numerical methods often relied on hand interpolation formulas, using data from large printed tables. Since the mid-20th century, computers calculate the required functions instead, but many of the same formulas continue to be used in software algorithms. The numerical point of view goes back to the earliest mathematical writings. A tablet from the Yale Babylonian Collection (YBC 7289), gives a sexagesimal numerical approximation of the square root of 2, the length of the diagonal in a unit square. Numerical analysis continues this long tradition: rather than giving exact symbolic answers translated into digits and applicable only to real-world measurements, approximate solutions within specified error bounds are used.
Numerical Recipes is the generic title of a series of books on algorithms and numerical analysis by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. In various editions, the books have been in print since 1986. The most recent edition was published in 2007.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Brown v. Board of Education in 1954.