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Practical Extrapolation Methods: Theory and Applications

General Information
Type.................: Ebook
Part Size............: 4,015,397 bytes

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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

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

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