Sequence Transformations [Paperback]

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.- (a) Methods of Detector Coefficients.- (b) Methods Using Barycenters.- (c) Limitation Results.- 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.- (a) Strength of an Accumulation Point.- (b) 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 SequenlĂ$