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The book gives a very clear and concise summary of the important fields of sequence transformations and convergence acceleration methods. Some of the outstanding features are: - precise definitions of algorithmic sequence transformations, - a study of the power of sequence transformations, - proof of negative results on acceleration methods (namely, that some sequence families are not accelerable), - new algorithms for convergence acceleration (in particular automatic selection procedures). For researchers and graduate students working in or with convergence acceleration methods and sequence transformations, this book is sure to become an important tool. This book is a contribution to the theory and practice of convergence acceleration methods. It gives a new survey point of view on the subject, with positive results (new method of acceleration) and negative results (proofs that some sequence families are not accelerable).
Front Matter
The Various Kinds of Algorithmic Sequence Transformations
Decidability and Undecidability in the Limit
Algorithms for Extracting Convergent Subsequences
The Partially Ordered Systems of Accelerable Families
Non-Accelerable Families of Sequences
Accelerating The Convergence of Linear Sequences
Automatic Selection of Sequence Transformations
Back Matter