Convergence Acceleration and Improvement by Regular Matrices

Ants Aasma ()
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Ants Aasma: Tallinn University of Technology, Department of Economics

A chapter in Current Topics in Summability Theory and Applications, 2016, pp 141-180 from Springer

Abstract: Abstract A new, nonclassical convergence acceleration concept, called $$\mu $$ μ -acceleration of convergence (where $$\mu $$ μ 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.

Keywords: Convergence acceleration; Improvement of convergence; Speed of convergence; Regular matrix methods; Order of approximation of Fourier expansions (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-0913-6_4

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DOI: 10.1007/978-981-10-0913-6_4

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