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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] [Amazon] |
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] [Amazon] |
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] [Amazon] |
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] [Amazon] |
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] [Amazon] |
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] [Amazon] |
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] [Amazon] |
Ray W
Ray or RAY may refer to: Fish * Ray (fish), any cartilaginous fish of the superorder Batoidea * Ray (fish fin anatomy), the bony or horny spine on ray-finned fish Science and mathematics * Half-line (geometry) or ray, half of a line split at an initial point * Directed half-line or ray, half of a directed or oriented line split at an initial point * Ray (graph theory), an infinite sequence of vertices such that each vertex appears at most once in the sequence and each two consecutive vertices in the sequence are the two endpoints of an edge in the graph * Ray (optics), an idealized narrow beam of light * Ray (quantum theory), an equivalence class of state-vectors representing the same state Arts and entertainment Music * The Rays, an American musical group active in the 1950s * Ray (musician), stage name of Japanese singer Reika Nakayama (born 1990) * Ray (girl group), a Japanese girl group formed in 2019 * Ray J, stage name of singer William Ray Norwood, Jr. (born 1981) * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Finite Element Method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
QR Factorization
In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix ''A'' into a product ''A'' = ''QR'' of an orthonormal matrix ''Q'' and an upper triangular matrix ''R''. QR decomposition is often used to solve the linear least squares (LLS) problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Cases and definitions Square matrix Any real square matrix ''A'' may be decomposed as : A = QR, where ''Q'' is an orthogonal matrix (its columns are orthogonal unit vectors meaning and ''R'' is an upper triangular matrix (also called right triangular matrix). If ''A'' is invertible, then the factorization is unique if we require the diagonal elements of ''R'' to be positive. If instead ''A'' is a complex square matrix, then there is a decomposition ''A'' = ''QR'' where ''Q'' is a unitary matrix (so the conjugate transpose If ''A'' has ''n'' linearly independent columns, then the first ''n'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Vera Kublanovskaya
Vera Nikolaevna Kublanovskaya (''née'' Totubalina; November 21, 1920 – February 21, 2012 ) was a Russian mathematician noted for her work on developing computational methods for solving spectral problems of algebra. She proposed the QR algorithm for computing eigenvalues and eigenvectors in 1961, which has been named as one of the ten most important algorithms of the twentieth century. This algorithm was proposed independently by the English computer scientist John G.F. Francis in 1961. Early life Kublanovskaya was born in November 1920 in Krokhona, a village near Belozersk in Vologda Oblast, Russian Soviet Federative Socialist Republic. She was born in a farming and fishing family as one of nine siblings. She died at the age of 91 years old in February 2012. Education Kublanovskaya started her tertiary education in 1939 at the Gertzen Pedagogical Institute in Leningrad. There, she was encouraged to pursue a career in mathematics. She moved on to study mathematics at Lenin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
John G
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope John ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
