Generalizations of Aitken's process for a certain class of sequences

Davide Buoso; Anna Karapiperi; Stefano Pozza

doi:10.1016/j.apnum.2014.12.002

Generalizations of Aitken's process for a certain class of sequences

Davide Buoso, Anna Karapiperi, Stefano Pozza

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we construct several sequence transformations whose kernels contain sequences of the form ^Sn=S+^an^λn, n=0,1,..., where S and λ are unknown parameters, and (^an) is a known sequence. These transformations generalize Aitken's ^Δ2 process. We provide certain sufficient conditions under which one of our transformations accelerates the convergence of certain types of sequences. Finally, we illustrate these theoretical results through several numerical experiments using diverging and converging sequences.

Original language	English
Pages (from-to)	38-54
Number of pages	17
Journal	Applied Numerical Mathematics
Volume	90
DOIs	https://doi.org/10.1016/j.apnum.2014.12.002
Publication status	Published - Apr 2015
Externally published	Yes

Keywords

Aitken's process
Convergence acceleration
Extrapolation
Semi-convergence

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10.1016/j.apnum.2014.12.002

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abstract = "In this paper, we construct several sequence transformations whose kernels contain sequences of the form Sn=S+anλn, n=0,1,..., where S and λ are unknown parameters, and (an) is a known sequence. These transformations generalize Aitken's Δ2 process. We provide certain sufficient conditions under which one of our transformations accelerates the convergence of certain types of sequences. Finally, we illustrate these theoretical results through several numerical experiments using diverging and converging sequences.",

keywords = "Aitken's process, Convergence acceleration, Extrapolation, Semi-convergence",

author = "Davide Buoso and Anna Karapiperi and Stefano Pozza",

note = "Publisher Copyright: {\textcopyright} 2014 Published by Elsevier B.V. on behalf of IMACS.",

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doi = "10.1016/j.apnum.2014.12.002",

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AU - Buoso, Davide

AU - Karapiperi, Anna

AU - Pozza, Stefano

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Y1 - 2015/4

N2 - In this paper, we construct several sequence transformations whose kernels contain sequences of the form Sn=S+anλn, n=0,1,..., where S and λ are unknown parameters, and (an) is a known sequence. These transformations generalize Aitken's Δ2 process. We provide certain sufficient conditions under which one of our transformations accelerates the convergence of certain types of sequences. Finally, we illustrate these theoretical results through several numerical experiments using diverging and converging sequences.

AB - In this paper, we construct several sequence transformations whose kernels contain sequences of the form Sn=S+anλn, n=0,1,..., where S and λ are unknown parameters, and (an) is a known sequence. These transformations generalize Aitken's Δ2 process. We provide certain sufficient conditions under which one of our transformations accelerates the convergence of certain types of sequences. Finally, we illustrate these theoretical results through several numerical experiments using diverging and converging sequences.

KW - Aitken's process

KW - Convergence acceleration

KW - Extrapolation

KW - Semi-convergence

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VL - 90

SP - 38

EP - 54

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Generalizations of Aitken's process for a certain class of sequences

Abstract

Keywords

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