Sequence Transformations

Sequence Transformations by Jean-Paul Delahaye.

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Bibliographic Details
Main Author: Delahaye, Jean-Paul (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988.
Edition:1st ed. 1988.
Series:Springer Series in Computational Mathematics, 11
Springer eBook Collection.
Subjects:
Numerical analysis.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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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