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" Sequence Transformations "
by Jean-Paul Delahaye.
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BL
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| Record Number
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751799
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b571758
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| Main Entry
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by Jean-Paul Delahaye.
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| Title & Author
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Sequence Transformations\ by Jean-Paul Delahaye.
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin Heidelberg, 1988
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| Series Statement
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Springer series in computational mathematics, 11.
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| Page. NO
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(XXI, 252p. 164 illus.).
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| ISBN
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3642613470
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: 9783642613470
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| Notes
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Bibliographic Level Mode of Issuance: Monograph.
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| Contents
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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 Monotones Sequences --; 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.
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| Subject
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Numerical analysis.
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| Subject
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Numerical Analysis.
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| LC Classification
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QA292.B954 1988
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| Added Entry
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Jean-Paul Delahaye
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