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Author: Philip J. Davis
Publisher: Courier Corporation
Published: 1975-01-01
Total Pages: 418
ISBN-13: 0486624951
DOWNLOAD EBOOKIntermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.
Author: David P. Williamson
Publisher: Cambridge University Press
Published: 2011-04-26
Total Pages: 518
ISBN-13: 9780521195270
DOWNLOAD EBOOKDiscrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
Author: Theodore J. Rivlin
Publisher: Courier Corporation
Published: 1981-01-01
Total Pages: 164
ISBN-13: 9780486640693
DOWNLOAD EBOOKMathematics of Computing -- Numerical Analysis.
Author: Harold Cohen
Publisher: Springer Science & Business Media
Published: 2011-09-28
Total Pages: 493
ISBN-13: 1441998365
DOWNLOAD EBOOKThis book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
Author: Vijay V. Vazirani
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 380
ISBN-13: 3662045656
DOWNLOAD EBOOKCovering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.
Author: George Anastassiou
Publisher: CRC Press
Published: 1992-04-24
Total Pages: 558
ISBN-13: 9780824787080
DOWNLOAD EBOOKContains the proceedings of the March 1991 annual conference of the Southeastern Approximation Theorists, in Memphis, Tenn. The 34 papers discuss topics of interest to graduate and professional numerical analysts, applied and industrial mathematicians, engineers, and other scientists such as splines
Author: Lloyd N. Trefethen
Publisher: SIAM
Published: 2013-01-03
Total Pages: 295
ISBN-13: 9781611972405
DOWNLOAD EBOOKAn original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.
Author: Vivek S. Borkar
Publisher: Springer
Published: 2009-01-01
Total Pages: 177
ISBN-13: 938627938X
DOWNLOAD EBOOKAuthor: Claude Brezinski
Publisher: Springer Nature
Published: 2020-11-30
Total Pages: 410
ISBN-13: 3030584186
DOWNLOAD EBOOKThis book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.
Author: O. C. Zienkiewicz
Publisher: Courier Corporation
Published: 2013-04-22
Total Pages: 356
ISBN-13: 048631801X
DOWNLOAD EBOOKA powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.
