| Description |
xxii, 519 pages ; 26 cm |
| Series |
Cambridge monographs on applied and computational mathematics ; 10 |
|
Cambridge monographs on applied and computational mathematics ; 10
|
| Contents |
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 GREP8. Analytic study of GREP (1): slowly varying A(y ŒF(1)9. Analytic study of GREP(1): quickly varying A(y ŒF(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 D2- process, and lubkin W- transformation. 16. The shanks transformation. 17. The padetable. 18. Generalizations of pade approximants. 19. The levin L - and S-transformations. 20. The wynn r- and brezinski q-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 |
| Summary |
An important problem that arises in many scientific and engineering applications is that of finding or approximating the so-called limits of infinite sequences Am. In most cases these sequences converge to their limits very slowly. In other words, to approximate the limits in question with reasonable accuracy one needs to compute a large number of the terms of Am, and this is an expensive proposition. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms of Am. This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. Its importance is rooted in the fact that the methods it discusses are geared towards problems that arise commonly 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, and also shows how to apply these methods to obtain best results |
| Notes |
Also known with subtitle: Their mathematical theory and application |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Extrapolation.
|
| Author |
MyiLibrary.
|
| LC no. |
2002024669 |
| ISBN |
0521661595 : |
|
