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Timeline Of Numerical Analysis After 1945
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. 1940s * Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis. * Crank–Nicolson method was developed by Crank and Nicolson. * Dantzig introduces the simplex method (voted one of the top 10 algorithms of the 20th century) in 1947. * Turing formulated the LU decomposition method. 1950s * Successive over-relaxation was devised simultaneously by D.M. Young Jr. and by H. Frankel in 1950. * Hestenes, Stiefel, and Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods. Voted one of the top 10 algorithms of the 20th century. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Computer
A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as ''programs'', which enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems, including simple special-purpose devices like microwave ovens and remote controls, and factory devices like industrial robots. Computers are at the core of general-purpose devices such as personal computers and mobile devices such as smartphones. Computers power the Internet, which links billions of computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Householder Matrix
In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder. Definition Operator and transformation The Householder operator may be defined over any finite-dimensional inner product space V with inner product \langle \cdot, \cdot \rangle and unit vector u\in V as : H_u(x) := x - 2\,\langle x,u \rangle\,u\,. It is also common to choose a non-unit vector q \in V, and normalize it directly in the Householder operator's expression: :H_q \left ( x \right ) = x - 2\, \frac\, q \,. Such an operator is linear and self-adjoint. If V=\mathbb^n, note that the reflection hyperplane can be defined by its ''normal vector'', a unit vector \vec v\in V (a vector with length 1) that is orthogonal to the hyperplane. The reflection of a point x about th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MacCormack Method
In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. The MacCormack method is elegant and easy to understand and program. The algorithm The MacCormack method is designed to solve hyperbolic partial differential equations of the form : \frac + \frac = 0 To update this equation one timestep \Delta t on a grid with spacing \Delta x at grid cell i , the MacCormack method uses a "predictor step" and a "corrector step", given below : \begin &u_i^p = u^n_i - \frac\left(f^n_ - f^n_i\right) \\ &u^_i = \frac(u^n_i + u^p_i) - \frac(f^p_i - f^p_) \end Linear Example To illustrate the algorithm, consider the following first order hyperbolic equation : \qquad \frac + a \frac = 0 . The application of MacCormack method to the above equation procee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Computer Library Center
OCLC, Inc. See also: is an American nonprofit cooperative organization "that provides shared technology services, original research, and community programs for its membership and the library community at large". It was founded in 1967 as the Ohio College Library Center, then became the Online Computer Library Center as it expanded. In 2017, the name was formally changed to OCLC, Inc. OCLC and thousands of its member libraries cooperatively produce and maintain WorldCat, the largest online public access catalog in the world. OCLC is funded mainly by the fees that libraries pay (around $217.8 million annually in total ) for the many different services it offers. OCLC also maintains the Dewey Decimal Classification system. History OCLC began in 1967, as the Ohio College Library Center, through a collaboration of university presidents, vice presidents, and library directors who wanted to create a cooperative, computerized network for libraries in the state of Ohio. The gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abramowitz And Stegun
''Abramowitz and Stegun'' (''AS'') is the informal name of a 1964 mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST). Its full title is ''Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables''. A digital successor to the Handbook was released as the " Digital Library of Mathematical Functions" (DLMF) on 11 May 2010, along with a printed version, the '' NIST Handbook of Mathematical Functions'', published by Cambridge University Press. Overview Since it was first published in 1964, the 1046-page ''Handbook'' has been one of the most comprehensive sources of information on special functions, containing definitions, identities, approximations, plots, and tables of values of numerous functions used in virtually all fields of applied mathematics. The notation used in the ''Handbook'' is the '' de facto'' standard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Analysis
Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on physical structures and their components. In contrast to theory of elasticity, the models used in structural analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
