Summary
An analogue of Aitken's Δ2 method, suitable for vector sequences, is proposed. Aspects of the numerical performance of the vector ε-algorithm, based on using the Moore-Penrose inverse, are investigated. The fact that the denominator polynomial associated with a vector Padé approximant is the square of its equivalent in the scalar case is shown to be a source of approximation error. In cases where the convergence of the vector sequence is dominated by real eigenvalues, a hybrid form of the vector Padé approximant, having a denominator polynomial of minimal degree, is proposed and its effectiveness is demonstrated on several standard examples.
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Graves-Morris, P.R. Extrapolation methods for vector sequences. Numer. Math. 61, 475–487 (1992). https://doi.org/10.1007/BF01385521
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DOI: https://doi.org/10.1007/BF01385521