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＜E-Book＞
Sequence Transformations / by Jean-Paul Delahaye
(Springer Series in Computational Mathematics. ISSN:21983712 ; 11)

Edition	1st ed. 1988.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1988
Language	English
Size	XXI, 252 p : online resource
Authors	*Delahaye, Jean-Paul author SpringerLink (Online service)
Subjects	LCSH:Numerical analysis FREE:Numerical Analysis
Notes	1 The Various Kinds of Algorithmic Sequence Transformations -- 1 — Sequence Transformations -- 2 — Algorithms for Sequences and Algorithmic Transformations -- 3 — k-Normal Algorithms and k-Normal Transformations -- 4 — k-Memories Algorithms and k-Memories Transformations -- 5 — k-Stationary Algorithms and k-Stationary Transformations -- 6 — Rational Transformations and Linear Transformations -- 7 — Diagram of Inclusions -- References -- 2 Decidability and Undecidability in the Limit -- 1 — Definitions and the Normalisation Theorem -- 2 — Problems Concerning Convergence, Turbulence and Periodicity of Sequences -- 3 — Algorithms for Counting the Number of Accumulation Points -- 4 — Algorithms for Determining the Period of an Asymptotically Periodic Sequence -- 5 — Families of Sequences of Iterations -- 6 — Two General Results Concerning the Decidability in the Limit -- Appendix 1 — Strength of an Accumulation Point and Quickness of a Sequence -- Appendix 2 — Decidability in the Limit and Recursivity. -- Appendix 3 — Decidability of the Convergence, Turbulence and Asymptotic Periodicity of a Continuous Function -- References -- 3 Algorithms for Extracting Convergent Subsequences -- 1 — T-Algorithms -- 2 — S-Algorithms -- 3 — U-Algorithms -- 4 — Limitation Results -- References -- 4 The Partially Ordered Systems of Accelerable Families -- 1 — Acceleration Velocity, Acceleration, Prediction -- 2 — Transformations for Convergence Acceleration, Accelerable Families -- 3 — Examples of Accelerable Families of Sequences -- 4 — Relationships Between the Ordered Systems of Accelerable Families -- 5 — Maximal Accelerable Families -- References -- 5 Non-Accelerable Families of Sequences -- 1 — Remanence and First Applications -- 2 — Families of MonotonesSequences -- 3 — Alternating and Oscillating Sequences -- 4 — Families of Linearly Convergent Sequences -- 5 — Families of Logarithmically Convergent Sequences -- 6 — Table of Results -- References -- 6 Accelerating the Convergence of Linear Sequences -- 1 — Linearly Convergent and Periodico-Linearly Convergent Sequences -- 2 — Acceleration of Periodico-Linear Sequences -- 3 — Optimality of the ?2 of Aitken -- References -- 7 Automatic Selection of Sequence Transformations -- 1 — General Methods -- 2 — Automatic Choice of Sequences of Parameters in the Richardson Extrapolation -- References HTTP:URL=https://doi.org/10.1007/978-3-642-61347-0

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