Acceleration techniques

R. Albrecht et al., Eds., Validation Numerics: Theory and Applications (Springer, Berlin, 1993) 11--32; 67--78.

F.L. Bauer, Nonlinear sequence transformations, in: Approximation of Functions (Elsevier, Amsterdam, 1965) 134--151.

I.S. Berezin and N.P. Zhidkov, Computing Methods, Vol. 2 (Pergamon Press, Oxford, 1965) Chapter 7.

R. Bhattacharya, D. Roy and S. Bhowmick, Finding roots using divergent functional iteration, Comput. Phys. Comm. 69 (1992) 339--346.

W. Kotzé, Notes on numerical analysis, IV. On accelerating iteration procedures with superlinear convergence, Canad. Math. Bull. 7 (1964) 425--430.

G.R. Lindfield and J.E.T. Penny, Microcomputers in Numerical Analysis (Wiley, New York, 1989) Chapter 2.

I. Manning, A method for improving iteration procedures, Proc. Cambridge Philos. Soc. 63 (1967) 183--186.

J.W. Schmidt, Asymptotische Einschliessung bei konvergenzbeschleunigenden Verfahren, Numer. Math. 8 (1966) 105--113; ibid. 11 (1968) 53--56.

E.L. Stiefel, An Introduction to Numerical Mathematics (Academic Press, New York, 1963).

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1980) 270--299.

G.M. Trojan, Lower bounds and fast algorithms for sequence acceleration, J. Assoc. Comput. Mach. 31 (1984) 329--335.

J.S. Vandergraft, Introduction to Numerical Computations (Prentice-Hall, Englewood Cliffs, NJ, 1964).

R. Wait, The Numerical Solution of Algebraic Equations (Wiley, Chichester, 1979).

G. Walz, Asymptotic expansions and acceleration of convergence for higher order iteration processes, Numer. Math. 59 (1991) 529--540.

P. Wynn, On a device for computing the em(Sn) transformation, Math. Tables Aids Comput. 10 (1956) 91--95.

P. Wynn, On a Procrustean technique for the numerical transformation of slowly convergent sequences and series, Proc. Cambridge Philos. Soc. 52 (1956) 663--671.