Table of 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 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 Δ2-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 ρ- and Brezinski θ-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.

Promotional Information

This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods.

Reviews

'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