Search results for: analytic-computational-complexity

Analytic Computational Complexity

Author : J.F. Traub
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Analytic Computational Complexity contains the proceedings of the Symposium on Analytic Computational Complexity held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7-8, 1975. The symposium provided a forum for assessing progress made in analytic computational complexity and covered topics ranging from strict lower and upper bounds on iterative computational complexity to numerical stability of iterations for solution of nonlinear equations and large linear systems. Comprised of 14 chapters, this book begins with an introduction to analytic computational complexity before turning to proof techniques used in analytic complexity. Subsequent chapters focus on the complexity of obtaining starting points for solving operator equations by Newton's method; maximal order of multipoint iterations using n evaluations; the use of integrals in the solution of nonlinear equations in N dimensions; and the complexity of differential equations. Algebraic constructions in an analytic setting are also discussed, along with the computational complexity of approximation operators. This monograph will be of interest to students and practitioners in the fields of applied mathematics and computer science.

Recent Problems and Results in Analytic Computational Complexity

Author : B. Kacewicz
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Applied and Computational Complex Analysis Volume 3

Author : Peter Henrici
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Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Topics in Computational Complexity and the Analysis of Algorithms

Author : Richard P. Brent
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Analytic Computational Complexity

Author : Joseph F. Traub
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Pi and the AGM

Author : Jonathan M. Borwein
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This book presents new research revealing the interplay between classical analysis and modern computation and complexity theory. Two intimately interwoven threads run through the text: the arithmetic-geometric mean (AGM) iteration of Gauss, Lagrange, and Legendre and the calculation of pi.

General Theory of Optimal Error Algorithms and Analytic Complexity Part B Iterative Information Model

Author : J. F. Traub
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This is the second of a series of papers in which we construct an information based general theory of optimal error algorithms and analytic computational complexity and study applications of the general theory. In our first paper we studied a general information' model; here we study an 'iterative information' model. We give a general paradigm, based on the pre-image set of an information operator, for obtaining a lower bound on the error of any algorithm using this information. We show that the order of information provides an upper bound on the order of any algorithm using this information. This upper bound order leads to a lower bound on the complexity index.

Applied and Computational Complex Analysis Volume 1

Author : Peter Henrici
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Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

A Survey of Recent Problems and Results in Analytical Computational Complexity

Author : Boleslaw Kacewicz
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Symposium on Analytic Computational Complexity Program and Abstracts Held at Carnegie Mellon University Pittsburgh Pennsylvania on April 7 8 1975

Author : J. F. Traub
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This is the program and abstracts of invited and contributed papers presented at a Symposium on Analytic Computational Complexity on April 7-8. The full texts of the invited papers and abstracts of the contributed papers will be published in the Proceedings by Academic Press in Fall, 1975.

Symposium on Analytic Computational Complexity Program and Abstracts

Author : J. F. Traub
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Pi and the AGM

Author : Jonathan M. Borwein
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Matrix Analytic Methods for Computations in Risk Theory

Author : Sung Soo Kim
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The introduction of matrix analytic methods in risk theory has marked a significant progress in computations in risk theory. Matrix analytic methods have proven to be powerful computational tools for numerically analyzing complex risk models that traditional methods often had difficulty with. This is particularly noteworthy in the modern age of advanced computing and big data. Moving away from the traditional view of collective risk theory, we can now consider risk models that comprise of many stochastic processes of which data are abundant. These models may fall under the existing class of risk models; however, these more realistic risk models involve a large number of variables which increases the computational complexity significantly. Matrix analytic methods can provide reliable computing algorithms for risk models of such computational complexity, which have not been numerically feasible to analyze with the traditional computational tools in risk theory. This thesis is dedicated to improving the accessibility of the matrix analytic methodology in risk theory and developing further generalizations of the existing matrix analytic methods in risk theory in the attempt to promote its computational use. Although the literature of matrix analytic methods in risk theory is in its early stage, it is believed that the advancement in computations in risk theory brought by the matrix analytic methods will broaden the spectrum of problems in the risk theory literature in the direction of more realistic and practical risk models and computational analyses of these models. This will make risk theory as a whole more appealing to practitioners and those who are looking for more advanced actuarial risk management tools.

Society for Industrial and Applied Mathematics Journal on Numerical Analysis

Author : Society for Industrial and Applied Mathematics
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General Theory of Optimal Error Algorithms and Analytic Complexity Part A General Information Model

Author : J. F. Traub
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This is the first of a series of papers constructing an information based general theory of optimal errors and analytic computational complexity. Among the applications are such traditionally diverse areas as approximation, boundary-value problems, quadrature, and nonlinear equations in a finite or infinite dimensional space. Traditionally algorithms are often derived by ad hoc criteria. The information based theory rationalizes the synthesis of algorithms by showing how to construct algorithms which minimize or nearly minimize the error. For certain classes of problems it shows how to construct algorithms (linear optimal error algorithms) which enjoy essentially optimal complexity with respect to all possible algorithms. The existence of strongly non-computable problems is demonstrated. In contrast with the gap theorem of recursively computable functions it is shown that every monotonic real function is the complexity of some problem.

Applied and Computational Complex Analysis Special functions

Author : Peter Henrici
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Applied and Computational Complex Analysis Volume 3

Author : Peter Henrici
File Size : 72.32 MB
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Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Australian Computer Journal

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The Complexity of Computational Problem Solving

Author : R. S. Anderssen
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Computational Complexity of iterative processes

Author : J. F. Traub
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The theory of optimal algorithmic processes is part of computational complexity. The paper deals with analytic computational complexity. The relation between the goodness of an iteration algorithm and its new function evaluation and memory requirements are analyzed. A new conjecture is stated. (Author).