Sequence Transformations

Inhaltsverzeichnis

• 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.
• 3 Algorithms for Extracting Convergent Subsequences.
• 1 — T-Algorithms.
• 2 — S-Algorithms.
• 3 — U-Algorithms.
• 4 — Limitation Results.
• 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.
• 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.
• 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.
• 7 Automatic Selection of Sequence Transformations.
• 1 — General Methods.
• 2 — Automatic Choice of Sequences of Parameters in the Richardson Extrapolation.