The rise and fall of the vector epsilon algorithm

DOI10.1007/BF02108462zbMath0798.65005OpenAlexW2033132621MaRDI QIDQ1315206

Peter R. Graves-Morris, Ian D. Coope

Publication date: 30 October 1994

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02108462

zbMATH Keywords

numerical exampleconvergence accelerationnumerical stabilityvector epsilon algorithm

Mathematics Subject Classification ID

Convergence and divergence of series and sequences of functions (40A30) Extrapolation to the limit, deferred corrections (65B05)

Related Items (12)

A review of Padé methods for the acceleration of convergence of a sequence of vectors ⋮ A new approach to acceleration of convergence of a sequence of vectors ⋮ The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods ⋮ Epsilon-algorithm and eta-algorithm of generalized inverse function-valued Padé approximants using for solution of integral equations ⋮ Introduction to the improved Levin-type algorithms for accelerating convergence of sequence. ⋮ Problems and progress in vector Padé approximation ⋮ Similarities of the integral Padé approximants. II ⋮ Solution of integral equations using Padé type approximants ⋮ A family of the functional epsilon algorithms for accelerating convergence ⋮ A family of Padé-type approximants for accelerating the convergence of sequences ⋮ Similarities of the integral Padé approximants ⋮ Introduction to the improved functional epsilon algorithm

Cites Work

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• Vector valued rational interpolants. I
• Solution of integral equations using generalised inverse, function-valued Padé approximants. I
• Padé-type approximation and general orthogonal polynomials
• The optimal \(\omega\) is not best for the SOR iteration method
• Row convergence theorems for generalised inverse vector-valued Padé approximants
• Degeneracies of generalized inverse, vector-valued Padé approximants
• Extrapolation methods for vector sequences
• Généralisations de la transformation de Shanks, de la table de Padé et de l'\(\varepsilon\)-algorithme
• Vector-valued, rational interpolants. III
• A note on the \(\epsilon\)-algorithm
• Continued fractions whose coefficients obey a non-commutative law of multiplication
• Acceleration Techniques for Iterated Vector and Matrix Problems
• Extrapolation Methods for Vector Sequences

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