1 The Various Kinds of Algorithmic Sequence Transformations -- 1 โ Sequence Transformations -- 2 โ Algorithms for Sequences and Algorithmic Transformations -- 3 โ k-Normal Algorithms and k-Normal Transformations -- 4 โ k-Memories Algorithms and k-Memories Transformations -- 5 โ k-Stationary Algorithms and k-Stationary Transformations -- 6 โ Rational Transformations and Linear Transformations -- 7 โ Diagram of Inclusions -- References -- 2 Decidability and Undecidability in the Limit -- 1 โ Definitions and the Normalisation Theorem -- 2 โ Problems Concerning Convergence, Turbulence and Periodicity of Sequences -- 3 โ Algorithms for Counting the Number of Accumulation Points -- 4 โ Algorithms for Determining the Period of an Asymptotically Periodic Sequence -- 5 โ Families of Sequences of Iterations -- 6 โ Two General Results Concerning the Decidability in the Limit -- Appendix 1 โ Strength of an Accumulation Point and Quickness of a Sequence -- Appendix 2 โ Decidability in the Limit and Recursivity. -- Appendix 3 โ Decidability of the Convergence, Turbulence and Asymptotic Periodicity of a Continuous Function -- References -- 3 Algorithms for Extracting Convergent Subsequences -- 1 โ T-Algorithms -- 2 โ S-Algorithms -- 3 โ U-Algorithms -- 4 โ Limitation Results -- References -- 4 The Partially Ordered Systems of Accelerable Families -- 1 โ Acceleration Velocity, Acceleration, Prediction -- 2 โ Transformations for Convergence Acceleration, Accelerable Families -- 3 โ Examples of Accelerable Families of Sequences -- 4 โ Relationships Between the Ordered Systems of Accelerable Families -- 5 โ Maximal Accelerable Families -- References -- 5 Non-Accelerable Families of Sequences -- 1 โ Remanence and First Applications -- 2 โ Families of Monotones Sequences -- 3 โ Alternating and Oscillating Sequences -- 4 โ Families of Linearly Convergent Sequences -- 5 โ Families of Logarithmically Convergent Sequences -- 6 โ Table of Results -- References -- 6 Accelerating the Convergence of Linear Sequences -- 1 โ Linearly Convergent and Periodico-Linearly Convergent Sequences -- 2 โ Acceleration of Periodico-Linear Sequences -- 3 โ Optimality of the ?2 of Aitken -- References -- 7 Automatic Selection of Sequence Transformations -- 1 โ General Methods -- 2 โ Automatic Choice of Sequences of Parameters in the Richardson Extrapolation -- References

1. Mathematics
2. Numerical analysis
3. Mathematics
4. Numerical Analysis