|
Chebfun
Chebfun is a free/open-source software system written in MATLAB for numerical computation with functions of a real variable. It is based on the idea of overloading MATLAB's commands for vectors and matrices to analogous commands for functions and operators. Thus, for example, whereas the SUM command in MATLAB adds up the elements of a vector, the SUM command in Chebfun evaluates a definite integral. Similarly the backslash command in MATLAB becomes a Chebfun command for solving differential equations. The mathematical basis of Chebfun is numerical algorithms involving piecewise polynomial interpolants and Chebyshev polynomials, and this is where the name "Cheb" comes from. The package aims to combine the feel of symbolic computing systems like Maple and Mathematica with the speed of floating-point numerics. The Chebfun project is based in the Mathematical Institute at the University of Oxford The University of Oxford is a collegiate university, collegiate research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chebyshev Polynomials
The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind T_n are defined by T_n(\cos \theta) = \cos(n\theta). Similarly, the Chebyshev polynomials of the second kind U_n are defined by U_n(\cos \theta) \sin \theta = \sin\big((n + 1)\theta\big). That these expressions define polynomials in \cos\theta is not obvious at first sight but can be shown using de Moivre's formula (see below). The Chebyshev polynomials are polynomials with the largest possible leading coefficient whose absolute value on the interval is bounded by 1. They are also the "extremal" polynomials for many other properties. In 1952, Cornelius Lanczos showed that the Chebyshev polynomials are important in approximation theory for the solution of linear systems; the roots of , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Software
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find 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 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 simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BSD Licenses
BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. This is in contrast to copyleft licenses, which have share-alike requirements. The original BSD license was used for its namesake, the Berkeley Software Distribution (BSD), a Unix-like operating system. The original version has since been revised, and its descendants are referred to as modified BSD licenses. BSD is both a license and a class of license (generally referred to as BSD-like). The modified BSD license (in wide use today) is very similar to the license originally used for the BSD version of Unix. The BSD license is a simple license that merely requires that all code retain the BSD license notice if redistributed in source code format, or reproduce the notice if redistributed in binary format. The BSD license (unlike some other licenses e.g. GPL) does not require that source code be distributed at all. Terms In addition to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free And Open Source Software
Free and open-source software (FOSS) is software available under a Software license, license that grants users the right to use, modify, and distribute the software modified or not to everyone free of charge. FOSS is an inclusive umbrella term encompassing free software and open-source software. The rights guaranteed by FOSS originate from the "Four Essential Freedoms" of ''The Free Software Definition'' and the criteria of ''The Open Source Definition''. All FOSS can have publicly available source code, but not all source-available software is FOSS. FOSS is the opposite of proprietary software, which is licensed restrictively or has undisclosed source code. The historical precursor to FOSS was the hobbyist and academic public domain software ecosystem of the 1960s to 1980s. Free and open-source operating systems such as Linux distributions and descendants of BSD are widely used, powering millions of server (computing), servers, desktop computer, desktops, smartphones, and othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maple (software)
Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation. Maple's capacity for symbolic computing include those of a general-purpose computer algebra system. For instance, it can manipulate mathematical expressions and find symbolic solutions to certain problems, such as those arising from ordinary and partial differential equations. Maple is developed commercially by the Canadian software company Maplesoft. The name 'Maple' is a reference to the software's Canadian heritage. Overview Core functionality Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematica
Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in ''Mathematica''. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast. There is a substantial literature on the development of computer algebra systems (CAS). __TOC_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Oxford
The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest universities in continuous operation, second-oldest continuously operating university globally. It expanded rapidly from 1167, when Henry II of England, Henry II prohibited English students from attending the University of Paris. When disputes erupted between students and the Oxford townspeople, some Oxford academics fled northeast to Cambridge, where they established the University of Cambridge in 1209. The two English Ancient university, ancient universities share many common features and are jointly referred to as ''Oxbridge''. The University of Oxford comprises 43 constituent colleges, consisting of 36 Colleges of the University of Oxford, semi-autonomous colleges, four permanent private halls and three societies (colleges that are depar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lloyd N
Lloyd, Lloyd's, or Lloyds may refer to: People * Lloyd (name), a variation of the Welsh word ' ("grey") or ' ** List of people with given name Lloyd ** List of people with surname Lloyd * Lloyd (singer) (born 1986), American singer Places United States * Lloyd, Florida * Lloyd, Kentucky * Lloyd, Montana * Lloyd, New York * Lloyd, Ohio * Lloyds, Alabama * Lloyds, Maryland * Lloyds, Virginia Elsewhere * Lloydminster, or "Lloyd", straddling the provincial border between Alberta and Saskatchewan, Canada Companies and businesses Derived from Lloyd's Coffee House *Lloyd's Coffee House, a London meeting place for merchants and shipowners between about 1688 and 1774 * Lloyd's of London, a British insurance market ** ''Lloyd's of London'' (film), a 1936 film about the insurance market ** Lloyd's building, its headquarters ** Lloyd's Agency Network * ''Lloyd's List'', a website and 275-year-old daily newspaper on shipping and global trade ** ''Lloyd's List Intelligence'' (f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
