Abstract:
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.
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