Sequence Transformations: Springer Series in Computational Mathematics, cartea 11

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.