, Volume 61, Issue 1, pp 475-487

Extrapolation methods for vector sequences

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.