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Eugene Salamin (mathematician)
Eugene Salamin is a mathematician who discovered (independently with Richard Brent) the Salamin–Brent algorithm, used in high-precision calculation of pi. Eugene Salamin worked on alternatives to increase accuracy and minimize computational processes through the use of quaternions. Benefits may include: # the design of spatio-temporal databases; # numerical mathematical methods that traditionally prove unsuccessful due to buildup of computational error; # therefore, may be applied to applications involving genetic algorithms and evolutionary computation In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, th ..., in general. Publications See also * HAKMEM References {{DEFAULTSORT:Salamin, Eugene 20th-century American mathematicians Year of birth missing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Brent (scientist)
Richard Peirce Brent is an Australian mathematician and computer scientist. He is an emeritus professor at the Australian National University. From March 2005 to March 2010 he was a Federation Fellow at the Australian National University. His research interests include number theory (in particular factorisation), random number generators, computer architecture, and analysis of algorithms. In 1973, he published a root-finding algorithm (an algorithm for solving equations numerically) which is now known as Brent's method. In 1975 he and Eugene Salamin independently conceived the Salamin–Brent algorithm, used in high-precision calculation of \pi. At the same time, he showed that all the elementary functions (such as log(''x''), sin(''x'') etc.) can be evaluated to high precision in the same time as \pi (apart from a small constant factor) using the arithmetic-geometric mean of Carl Friedrich Gauss. In 1979 he showed that the first 75 million complex zeros of the Riema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two '' directed lines'' in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative. Quaternions are generally represented in the form :a + b\ \mathbf i + c\ \mathbf j +d\ \mathbf k where , and are real numbers; and , and are the ''basic quaternions''. Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, and crystallographic texture analysis. They can be used alongside other methods of rotation, such as Euler angles and rotation matrices, or as an alternative to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatio-temporal Database
A spatiotemporal database is a database that manages both space and time information. Common examples include: * Tracking of moving objects, which typically can occupy only a single position at a given time. * A database of wireless communication networks, which may exist only for a short timespan within a geographic region. * An index of species in a given geographic region, where over time additional species may be introduced or existing species migrate or die out. * Historical tracking of plate tectonic activity. Spatiotemporal databases are an extension of spatial databases and temporal databases. A spatiotemporal database embodies spatial, temporal, and spatiotemporal database concepts, and captures spatial and temporal aspects of data and deals with: * geometry changing over time and/or * location of objects moving over invariant geometry (known variously as ''moving objects databases'' or real-time locating systems). Implementations Although there exist numerous relationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Algorithm
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, etc. Methodology Optimization problems In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Computation
In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character. In evolutionary computation, an initial set of candidate solutions is generated and iteratively updated. Each new generation is produced by stochastically removing less desired solutions, and introducing small random changes. In biological terminology, a population of solutions is subjected to natural selection (or artificial selection) and mutation. As a result, the population will gradually evolve to increase in fitness, in this case the chosen fitness function of the algorithm. Evolutionary computation techniques can produce highly optimized solutions in a wide range of problem settings, making them popula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HAKMEM
HAKMEM, alternatively known as AI Memo 239, is a February 1972 "memo" (technical report) of the MIT AI Lab containing a wide variety of hacks, including useful and clever algorithms for mathematical computation, some number theory and schematic diagrams for hardware – in Guy L. Steele's words, "a bizarre and eclectic potpourri of technical trivia". Contributors included about two dozen members and associates of the AI Lab. The title of the report is short for "hacks memo", abbreviated to six upper case characters that would fit in a single PDP-10 machine word (using a six-bit character set). History HAKMEM is notable as an early compendium of algorithmic technique, particularly for its practical bent, and as an illustration of the wide-ranging interests of AI Lab people of the time, which included almost anything other than AI research. HAKMEM contains original work in some fields, notably continued fractions. Introduction :Compiled with the hope that a record of the ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
