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Erschienen in:
An Introduction to Summability Methods Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Convergence Acceleration and Improvement by Regular Matrices

verfasst von : Ants Aasma

Erschienen in: Current Topics in Summability Theory and Applications

Verlag: Springer Singapore

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Abstract

A new, nonclassical convergence acceleration concept, called \(\mu \)-acceleration of convergence (where \(\mu \) is a positive monotonically increasing sequence), is introduced and compared with the classical convergence acceleration concept. It is shown that this concept allows to compare the speeds of convergence for a larger set of sequences than the classical convergence acceleration concept. Also, regular matrix methods that improve and accelerate the convergence of sequences and series are studied. Some problems related to the speed of convergence of sequences and series with respect to matrix methods are discussed. Several theorems on the improvement and acceleration of the convergence are proved. As an application, the results obtained are used to increase the order of approximation of Fourier expansions and Zygmund means of Fourier expansions in certain Banach spaces.

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Vorheriges Kapitel Summability and Convergence Using Ideals
Nächstes Kapitel On Summability, Multipliability, and Integrability
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Metadaten
Titel
Convergence Acceleration and Improvement by Regular Matrices
verfasst von
Ants Aasma
Copyright-Jahr
2016
Verlag
Springer Singapore
Buch
Current Topics in Summability Theory and Applications

Print ISBN: 978-981-10-0912-9

Electronic ISBN: 978-981-10-0913-6

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-981-10-0913-6_4