Practical Extrapolation Methods Theory and Applications This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. Avram Sidi (Author) 9780521661591, Cambridge University Press Hardback, published 5 June 2003 542 pages25.5 x 17.9 x 3.8 cm, 1.22 kg 'The book is an excellent support for the theoretical and practical studies of the speed-up methods based on extrapolation. It is a useful book for mathematicians interested in this field of research, but it can be used successfully by computer scientists and engineers.' Zentralblatt MATH 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 state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems. Preface Introduction Part I. The Richardson Extrapolation Process and Its Generalizations: 1. The richardson extrapolation process 2. Additional topics in Richardson extrapolation 3. First generalization of the Richardson extrapolation process 4. GREP: further generalization of the Richardson extrapolation process 5. The d-transformation: a GREP for infinite-range integrals 6. The d-transformation: a GREP for infinite series and sequences 7. Recursive algorithms for GREP 8. Analytic study of GREP (1): slowly varying A(y) ? F(1) 9. Analytic study of GREP(1): quickly varying A(y) ? F(1) 10: Efficient use of GREP(1): applications to the D(1)-, d(1)- and d(m)-transformations 11. Reduction of the d-transformation for oscillatory infinite-range integrals: the D-, D-, W-, and mW-transformations 12. Acceleration of convergence of power series by the d-transformation: rational d-approximants 13. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: the complex series approach with APS 14. Special topics in Richardson extrapolation Part II. Sequence Transformations: 15. The Euler transformation, Aitken ?2-process, and Lubkin W-transformation 16. The Shanks transformation 17. The Padé table 18. Generalizations of Padé approximants 19. The Levin L- and S-transformations 20. The Wynn ?- and Brezinski ?-algorithms 21. The g-transformation and its generalizations 22. The transformations of Overholt and Wimp 23. Confluent transformations 24. Formal theory of sequence transformations Part III. Further Applications: 25. Further applications of extrapolation methods and sequence transformations Part IV. Appendices: A. review of basic asymptotics B. The Laplace transform and Watson's lemma C. The gamma function D. Bernoulli numbers and polynomials and the Euler-Maclaurin formula E. The Riemann zeta function F. Some highlights of polynomial approximation theory G. A compendium of sequence transformations H. Efficient application of sequence transformations: Summary I. FORTRAN 77 program for the d(m)-transformation. Subject Areas: Numerical analysis [PBKS]
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