Bulletin of the American Mathematical Society

MathSciNet review: 1567593
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Book Information:

Author: Jet Wimp
Title: Sequence transformations and their applications
Additional book information: Mathematics in Science and Engineering, vol. 154, Academic Press, 1981, xix + 257 pp., $38.50. ISBN 0-12-757940-0.

Ralph P. Boas, Estimating remainders, Math. Mag. 51 (1978), no. 2, 83–89. MR 612186, DOI 10.2307/2690143

Claude Brezinski, Accélération de la convergence en analyse numérique, Lecture Notes in Mathematics, Vol. 584, Springer-Verlag, Berlin-New York, 1977 (French). MR 0455266

Claude Brezinski, Algorithmes d’accélération de la convergence, Collection Langages et Algorithmes de l’Informatique, Éditions Technip, Paris, 1978 (French). Étude numérique. MR 511657

Philip Calabrese, Classroom Notes: A Note on Alternating Series, Amer. Math. Monthly 69 (1962), no. 3, 215–217. MR 1531588, DOI 10.2307/2311056

B. Germain-Bonne, Transformations de suites, Rev. Française Automat. Informat. Recherche Opérationnelle 7 (1973), no. R-1, 84–90 (French, with Loose English summary). MR 0356440

6.

B. Germain-Bonne, Thesis, Univ. des Sciences et Techniques de Lille, 1978.

T. Hȧvie, Generalized Neville type extrapolation schemes, BIT 19 (1979), no. 2, 204–213. MR 537780, DOI 10.1007/BF01930850

8.

R. L. Higgins, Thesis, Drexel Univ., 1976.

Richard Johnsonbaugh, Summing an alternating series, Amer. Math. Monthly 86 (1979), no. 8, 637–648. MR 546176, DOI 10.2307/2321292

10.

E. E. Kummer, Eine neue methode, die numerischen summen langsam convergirenden reihen zu berechnen, J. Reine Angew. Math. 16 (1837), 206-214.

Mark A. Pinsky, Averaging an alternating series, Math. Mag. 51 (1978), no. 4, 235–237. MR 506726, DOI 10.2307/2689470

12.

D. F. Riddle, Calculus and analytic geometry (2nd ed.), Wadsworth, Belmont, California, 1974.

R. J. Schmidt, On the numerical solution of linear simultaneous equations by an iterative method, Philos. Mag. (7) 32 (1941), 369–383. MR 6231

Daniel Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. and Phys. 34 (1955), 1–42. MR 68901, DOI 10.1002/sapm19553411

William F. Trench, An algorithm for the inversion of finite Hankel matrices, J. Soc. Indust. Appl. Math. 13 (1965), 1102–1107. MR 189232

16.

R. R. Tucker, Thesis, Oregon State University, 1963.

Richard R. Tucker, The $\delta ^{2}$-process and related topics, Pacific J. Math. 22 (1967), 349–359. MR 218780

Richard R. Tucker, The $\delta ^{2}$-process and related topics. II, Pacific J. Math. 28 (1969), 455–463. MR 243220

19.

R. R. Tucker, A general theory of alternating series, 1986 (in preparation).

1.

R. P. Boas, Estimating remainders, Math. Magazine 51 (1978), 83-89. MR 0612186

2.

C. Brezinski, Accélération de la convergence en analyse numérique, Lecture Notes in Math., vol. 584, Springer-Verlag, Berlin and New York, 1977. MR 455266

3.

C. Brezinski, Algorithmes d'accélération de la convergence: Etude numérique, Editions Technip, Paris, 1978. MR 511657

4.

P. Calabrese, A note on alternating series, Amer. Math. Monthly 69 (1962), 215-217; repr. in Selected Papers in Calculus, 1968, pp. 352-353. MR 1531588

5.

B. Germain-Bonne, Transformations de suites, Rev. Française Automat. Informat. Recherche Opérationnelle 7 (1973), 84-94. MR 356440

6.

B. Germain-Bonne, Thesis, Univ. des Sciences et Techniques de Lille, 1978.

7.

T. Havie, Generalized neville type extrapolation schemes, BIT 19 (1979), 204-213. MR 537780

8.

R. L. Higgins, Thesis, Drexel Univ., 1976.

9.

R. Johnsonbaugh, Summing an alternating series, Amer. Math. Monthly 86 (1979), 637-648. MR 546176

10.

E. E. Kummer, Eine neue methode, die numerischen summen langsam convergirenden reihen zu berechnen, J. Reine Angew. Math. 16 (1837), 206-214.

11.

M. A. Pinsky, Averaging an alternating series, Math. Magazine 51 (1978), 235-237. MR 506726

12.

D. F. Riddle, Calculus and analytic geometry (2nd ed.), Wadsworth, Belmont, California, 1974.

13.

J. R. Schmidt, Philos. Mag. 32 (1941), 369-383. MR 6231

14.

D. Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34 (1955), 1-42. MR 68901

15.

W. F. Trench, An algorithm for the inversion of finite Hankel matrices, Siam. J. Appl. Math. 13 (1965), 1102-1107. MR 189232

16.

R. R. Tucker, Thesis, Oregon State University, 1963.

17.

R. R. Tucker, The δ, Pacific J. Math. 22 (1967), 349-359. MR 218780

18.

R. R. Tucker, The δ. II, Pacific J. Math. 28 (1969), 455-463. MR 243220

19.

R. R. Tucker, A general theory of alternating series, 1986 (in preparation).