Numerische Mathematik

, Volume 61, Issue 1, pp 475–487

Extrapolation methods for vector sequences

  • P. R. Graves-Morris

DOI: 10.1007/BF01385521

Cite this article as:
Graves-Morris, P.R. Numer. Math. (1992) 61: 475. doi:10.1007/BF01385521


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.

Mathematics Subject Classification (1991)


Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • P. R. Graves-Morris
    • 1
  1. 1.Department of MathematicsUniversity of BradfordBradfordUK