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**Sequence transformations. With an introduction by Claude Brezinski.**
*(English)*
Zbl 0652.65004

Springer series in Computational Mathematics, 11. Berlin etc.: Springer- Verlag. xxi, 252 p. (1988).

The first chapter contains several definitions that give a system of classes and subclasses of sequence transformations. Chapter 2 contains the following results: the normalization theorem which states the equivalence of algorithms for sequences and normal algorithms on problems of decidability in the limit; the decidability of some problems concerning convergence, periodicity and turbulence of sequences; algorithms for determining the period of an asymptotically periodic sequence and for counting the number of accumulation points of sequences. Chapter 3 is devoted to the problem of extracting convergent sequences from non convergent sequences.

Chapter 4 presents general aspects of the notions used in convergence acceleration, and the problem of maximal accelerable families is studied. The permancence property is applied to several families of monotone, linear or logarithmic sequences in chapter 5. In chapter 6, new algorithms are presented for accelerating the convergence of periodic linear sequences. In chapter 7 the author presents some methods for automatic selection among transformations for accelerating convergence and the selection of a good sequence of parameters for the Richardson process.

Chapter 4 presents general aspects of the notions used in convergence acceleration, and the problem of maximal accelerable families is studied. The permancence property is applied to several families of monotone, linear or logarithmic sequences in chapter 5. In chapter 6, new algorithms are presented for accelerating the convergence of periodic linear sequences. In chapter 7 the author presents some methods for automatic selection among transformations for accelerating convergence and the selection of a good sequence of parameters for the Richardson process.

Reviewer: N.Ţăndăreanu

### MSC:

65B05 | Extrapolation to the limit, deferred corrections |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |