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The Vector Epsilon Algorithm – a Residual Approach

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Abstract

We present an alternative to the vector ε-algorithm based on vector continued fractions and which is applicable when the sequence to be accelerated is generated by a one-point iteration function. These fractions are constructed in the language of Clifford algebras, which allow three-term recurrence relations. The new algorithm evidently has considerably greater numerical precision than the old one. Results from numerical experiments are reported.

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  1. Department of Mathematics, Napier University, 10 Colinton Road, Edinburgh, EH10 5DT, UK

    D.E. Roberts

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  1. D.E. Roberts
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Roberts, D. The Vector Epsilon Algorithm – a Residual Approach. Numerical Algorithms 29, 209–227 (2002). https://doi.org/10.1023/A:1014880510928

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