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Richard S. Varga
Richard Steven Varga (October 9, 1928 - February 25, 2022) was an American mathematician who specialized in numerical analysis and linear algebra. He was an Emeritus University Professor of Mathematical Sciences at Kent State University and an adjunct Professor at Case Western Reserve University. Varga was known for his contributions to many areas of mathematics, including Matrix (mathematics), matrix analysis, complex analysis, approximation theory, and Computational science, scientific computation. He was the author of the classic textbook ''Matrix Iterative Analysis''. Varga served as the Editor-in-Chief of the journal ''Electronic Transactions on Numerical Analysis'' (ETNA). Birth and education Richard Varga was born in Cleveland, Ohio of Hungarian people, Hungarian-born parents in 1928. He obtained a bachelor's degree in mathematics from Case Institute of Technology (present Case Western Reserve University) in 1950. Varga was a member of the collegiate wrestling team of Case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cleveland
Cleveland ( ), officially the City of Cleveland, is a city in the U.S. state of Ohio and the county seat of Cuyahoga County. Located in the northeastern part of the state, it is situated along the southern shore of Lake Erie, across the U.S. maritime border with Canada, northeast of Cincinnati, northeast of Columbus, and approximately west of Pennsylvania. The largest city on Lake Erie and one of the major cities of the Great Lakes region, Cleveland ranks as the 54th-largest city in the U.S. with a 2020 population of 372,624. The city anchors both the Greater Cleveland metropolitan statistical area (MSA) and the larger Cleveland–Akron–Canton combined statistical area (CSA). The CSA is the most populous in Ohio and the 17th largest in the country, with a population of 3.63 million in 2020, while the MSA ranks as 34th largest at 2.09 million. Cleveland was founded in 1796 near the mouth of the Cuyahoga River by General Moses Cleaveland, after whom the city was named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Matrix
In mathematics, a nonnegative matrix, written : \mathbf \geq 0, is a matrix in which all the elements are equal to or greater than zero, that is, : x_ \geq 0\qquad \forall . A positive matrix is a matrix in which all the elements are strictly greater than zero. The set of positive matrices is a subset of all non-negative matrices. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. A matrix which is both non-negative and is positive semidefinite is called a doubly non-negative matrix. A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via non-negative matrix factorization. Eigenvalues and eigenvectors of square positive matrices are described by the Perron–Frobenius theorem. Properties *The trace and every row and column sum/product of a nonnegative matrix is nonnegative. Inversion The inverse of any non-singul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Method
In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''n''-th approximation is derived from the previous ones. A specific implementation of an iterative method, including the Algorithm#Termination, termination criteria, is an algorithm of the iterative method. An iterative method is called convergent if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution (for example, solving a linear system of equations A\mathbf=\mathbf by Gaussian elimination). Iterative methods are often the only cho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Sum
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance. For a long time, the idea that such a potentially infinite summation could produce a finite result was considered paradoxical. This paradox was resolved using the concept of a limit during the 17th century. Zeno's paradox of Achilles and the tortoise illustrates this counterintuitive property of infinite sums: Achilles runs after a tortoise, but when he reaches the position of the tortoise at the beginning of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entire Function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric functions sine and cosine and their hyperbolic counterparts sinh and cosh, as well as derivatives and integrals of entire functions such as the error function. If an entire function has a root at , then , taking the limit value at , is an entire function. On the other hand, the natural logarithm, the reciprocal function, and the square root are all not entire functions, nor can they be continued analytically to an entire function. A transcendental entire function is an entire function that is not a polynomial. Properties Every entire function can be represented as a power series f(z) = \sum_^\infty a_n z^n that converges everywhere in the complex plane, hen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its Taylor series about ''x''0 converges to the function in some neighborhood for every ''x''0 in its domain. Definitions Formally, a function f is ''real analytic'' on an open set D in the real line if for any x_0\in D one can write : f(x) = \sum_^\infty a_ \left( x-x_0 \right)^ = a_0 + a_1 (x-x_0) + a_2 (x-x_0)^2 + a_3 (x-x_0)^3 + \cdots in which the coefficients a_0, a_1, \dots are real numbers and the series is convergent to f(x) for x in a neighborhood of x_0. Alternatively, a real analytic function is an infinitely differentiable function such that the Taylor series at any point x_0 in its domain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collegiate Wrestling
Collegiate wrestling (also known as folkstyle wrestling) is the form of wrestling practiced at the college and university level in the United States. This style of wrestling, with some slight modifications, is also practiced at high school and middle school levels, and also among younger participants. The rules and style of collegiate or folkstyle wrestling differs from other styles of wrestling that are practiced around the world such as those in the Olympic Games, freestyle wrestling and Greco-Roman wrestling. Women's wrestling at the US college level uses two different rulesets. The National Wrestling Coaches Association, whose women's division is now recognized by the NCAA as part of its Emerging Sports for Women program, uses the freestyle ruleset as defined by the sport's international governing body, United World Wrestling. The National Collegiate Wrestling Association, a separate governing body that conducts competition for colleges and universities parallel to but outsid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungarian People
Hungarians, also known as Magyars ( ; hu, magyarok ), are a nation and ethnic group native to Hungary () and Kingdom of Hungary, historical Hungarian lands who share a common Hungarian culture, culture, Hungarian history, history, Magyar tribes, ancestry, and Hungarian language, language. The Hungarian language belongs to the Uralic languages, Uralic language family. There are an estimated 15 million ethnic Hungarians and their descendants worldwide, of whom 9.6 million live in today's Hungary. About 2–3 million Hungarians live in areas that were part of the Kingdom of Hungary before the Treaty of Trianon in 1920 and are now parts of Hungary's seven neighbouring countries, Hungarians in Slovakia, Slovakia, Hungarians in Ukraine, Ukraine, Hungarians in Romania, Romania, Hungarians in Serbia, Serbia, Hungarians of Croatia, Croatia, Prekmurje, Slovenia, and Hungarians in Austria, Austria. Hungarian diaspora, Significant groups of people with Hungarian ancestry live in various oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Transactions On Numerical Analysis
''Electronic Transactions on Numerical Analysis'' is a peer-reviewed scientific open access journal publishing original research in applied mathematics with the focus on numerical analysis and scientific computing. It is published by the Kent State University and the Johann Radon Institute for Computational and Applied Mathematics (RICAM). Articles for this journal are published in electronic form on the journal's web site. The journal is one of the oldest scientific open access journals in mathematics. The Electronic Transactions on Numerical Analysis were founded in 1992 by Richard S. Varga, Arden Ruttan, and Lothar Reichel (all Kent State University) as a fully open access journal (no fee for reader or authors). The first issue appeared in September 1993. The current editors-in-chief are Lothar Reichel and Ronny Ramlau. Editors-in-chief * 1993–2008: Richard S. Varga * 1993–1998: Arden Ruttan * 2005–2013: Daniel Szyld * since 1993: Lothar Reichel * si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Science
Computational science, also known as scientific computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems. It is an area of science that spans many disciplines, but at its core, it involves the development of models and simulations to understand natural systems. * Algorithms ( numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve science (e.g., biological, physical, and social), engineering, and humanities problems * Computer hardware that develops and optimizes the advanced system hardware, firmware, networking, and data management components needed to solve computationally demanding problems * The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and information science In practical use, it is typically the application of computer simulation and other fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Theory
In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characterizing the approximation error, errors introduced thereby. Note that what is meant by ''best'' and ''simpler'' will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials. One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or Rational function, rational (ratio of polynomials) approximations. The objective is to make t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
