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Practical Extrapolation Methods Theory and Applications~tqw~ darksiderg

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******************************************************************************* Practical Extrapolation Methods: Theory and Applications ******************************************************************************* ------------------------------------------------------------------------------- General Information ------------------------------------------------------------------------------- Type.................: Ebook Part Size............: 4,015,397 bytes ------------------------------------------------------------------------------- Post Information ------------------------------------------------------------------------------- Posted by............: ~tqw~ ------------------------------------------------------------------------------- Release Notes ------------------------------------------------------------------------------- An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This book is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods it discusses are geared toward problems that commonly arise in scientific and engineering disciplines. It differs from existing books on the subject in that it concentrates on the most powerful nonlinear methods, presents in-depth treatments of them, and shows which methods are most effective for different classes of practical nontrivial problems; it also shows how to fine-tune these methods to obtain the best numerical results. This state-of-the-art reference on the theory and practice of extrapolation methods will interest mathematicians interested in the theory of the relevant methods as well as giving applied scientists and engineers a practical guide to applying speed-up methods in the solution of difficult computational problems. Avram Sidi is Professor is Numerical Analysis in the Computer Science Department at the Technion-Israel Institute of Technology and holds the Technion Administration Chair in Computer Science. He has published extensively in various areas of numerical analysis and approximation theory and in journals such asMathematics of Computation, SIAM Review, SIAM Journal on Numerical Analysis, Journal of Approximation Theory, Journal of Computational and Applied Mathematics, Numerische Mathematik, and Journal of Scientific Computing. Professor Sidi's work has involved the development of novel methods, their detailed mathematical analysis, design of efficient algorithms for their implementation, and their application to difficult practical problems. His methods and algorithms are successfully used in various scientific and engineering disciplines. Table of Contents Preface Introduction 1 I The Richardson Extrapolation Process and Its Generalizations 19 1 The Richardson Extrapolation Process 21 2 Additional Topics in Richardson Extrapolation 42 3 First Generalization of the Richardson Extrapolation Process 57 4 GREP: Further Generalization of the Richardson Extrapolation Process 81 5 The D-Transformation: A GREP for Infinite-Range Integrals 95 6 The d-Transformation: A GREP for Infinite Series and Sequences 121 7 Recursive Algorithms for GREP 158 8 Analytic Study of GREP 176 9 Analytic Study of GREP 203 10 Efficiency Use of GREP Applications to the D, and Transformations 212 11 Reduction of the D-Transformation for Oscillatory Infinite-Range 218 12 Acceleration of Convergence of Power Series by the d-Transformation: Rational d-Approximants 238 13 Acceleration of Convergence of Fourier and Generalized Fourier Series by the d-Transformation: The Complex Series Approach with APS 253 14 Special Topics in Richardson Extrapolation 263 II Sequence Transformations 277 15 The Euler Transformation, Aitken Process and Lubkin W-Transformation 279 16 The Shanks Transformation 297 17 The Pade Table 323 18 Generalizations of Pade Approximants 348 19 The Levin L- and Sidi S-Transformations 363 20 The Wynn [rho]- and Brezinski [theta]-Algorithms 375 21 The G-Transformation and Its Generalizations 384 22 The Transformations of Overholt and Wimp 390 23 Confluent Transformations 396 24 Formal Theory of Sequence Transformations 407 III Further Applications 413 25 Further Applications of Extrapolation Methods and Sequence Transformations 415 IV Appendices 457 A Review of Basic Asymptotics 459 B The Laplace Transform and Watson's Lemma 463 C The Gamma Function 465 D Bernoulli Numbers and Polynomials and the Euler-Maclaurin Formula 467 E The Riemann Zeta Function and the Generalized Zeta Function 477 F Some Highlights of Polynomial Approximation Theory 480 G A Compendium of Sequence Transformations 483 H Efficient Application of Sequence Transformations: Summary 488 I FORTRAN 77 Program for the d[superscript (m)]-Transformation 493 Bibliography 501 Index 515 Product Details * ISBN: 0521661595 * ISBN-13: 9780521661591 * Format: Hardcover, 519pp * Publisher: Cambridge University Press * Pub. Date: June 2003 ------------------------------------------------------------------------------- Install Notes ------------------------------------------------------------------------------- Adobe Acrobat Reader
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