A Survey of Shanks’ Extrapolation Methods and Their Applications
| Autor: | Claude Brezinski, Michela Redivo-Zaglia |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Sequence
Series (mathematics) sequence transformations Analytic continuation Extrapolation Acceleration methods sequence transformations Shanks’ transformation Padé approximation tensor tensor Sequence transformation Computational Mathematics Shanks’ transformation Transformation (function) Acceleration methods Applied mathematics Shanks transformation Limit (mathematics) Padé approximation Mathematics |
| Popis: | When a sequence or a series of scalars, vectors, matrices, tensors, is converging slowly to its limit, it can be transformed, by a sequence transformation, into a new sequence or a set of new sequences, which under some assumptions converges faster to the same limit. Such a transformation can even be applied to diverging sequences or series, thus providing its analytic continuation. Shanks’ transformation is a well known sequence transformation for accelerating the convergence of scalar sequences. In this survey, we explain its development, its various extensions, and its implementation. Several applications illustrate its effectiveness. |
| Databáze: | OpenAIRE |
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