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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 carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer 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. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, which links bil ... [...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. Its analogue over general inner product spaces is the Householder operator. Definition Transformation The reflection hyperplane can be defined by its ''normal vector'', a unit vector v (a vector with length 1) that is orthogonal to the hyperplane. The reflection of a point x about this hyperplane is the linear transformation: : x - 2\langle x, v\rangle v = x - 2v\left(v^\textsf x\right), where v is given as a column unit vector with Hermitian transpose v^\textsf. Householder matrix The matrix constructed from this transformation can be expressed in terms of an outer product as: : P = I - 2vv^\textsf is known as the Householder matrix, where I is the identity matrix. Proper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Computer Library Center
OCLC, Inc., doing business as OCLC, 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 (OPAC) 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 ... [...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 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithms
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space and ... [...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 the physical structures and their components. In contrast to theory of elasticity, the models used in structure 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] |
Ray W
Ray may refer to: Fish * Ray (fish), any cartilaginous fish of the superorder Batoidea * Ray (fish fin anatomy), a bony or horny spine on a fin Science and mathematics * Ray (geometry), half of a line proceeding from 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 J, stage name of singer William Ray Norwood, Jr. (born 1981) * ''Ray'' (Bump of Chicken album) * ''Ray'' (Frazier Chorus album) * ''Ray'' (L'Arc-en-Ciel album) * ''Rays'' (Michael Nesmith album) (former Monkee) * ''Ray'' (soundtrack), a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
The 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. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are 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 numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 orthogonal matrix ''Q'' and an upper triangular matrix ''R''. QR decomposition is often used to solve the linear least squares 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 If ''A'' has ''n'' linearly independent columns, then the first ''n'' columns of ''Q'' form an o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 1959. Early life Kublanovskaya was born in November 1920 in Krokhona, a village near Belozersk in Vologda Oblast, Russia. 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 Leningrad State University in 1945 and gradu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * 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 Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
