Further development of the new algorithms for accelerating the convergence of functional-type sequences

There are two aims of this paper. Firstly, we shall introduce the determinantal formulae for the new functional-type algorithms and secondly we shall demonstrate further development of the new functional-type algorithms namely, ρ-algorithms and ϕ-algorithms. We consider the use of the new algorithms...

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Vydané v:Applied mathematics and computation Ročník 186; číslo 1; s. 749 - 762
Hlavný autor: Thukral, R.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY Elsevier Inc 01.03.2007
Elsevier
Predmet:
Acceleration of convergence
Convergence acceleration
Exact sciences and technology
Improved functional epsilon algorithm
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
α, β, γ, δ, ϕ, ρ-algorithms
Improved functional epsilon algorithm
α, β, γ, δ, ϕ, ρ-algorithms
Convergence acceleration
a
Algorithm
Power series
Convergence
Functional
β
Numerical analysis
γ
δ
Applied mathematics
Development
ø
p-algorithms; Improved functional epsilon algorithm; Convergence acceleration
ISSN:0096-3003, 1873-5649
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Popis
Shrnutí:There are two aims of this paper. Firstly, we shall introduce the determinantal formulae for the new functional-type algorithms and secondly we shall demonstrate further development of the new functional-type algorithms namely, ρ-algorithms and ϕ-algorithms. We consider the use of the new algorithms to accelerate the convergence of functional-type sequences and their effectiveness for approximating the solution of a given power series is illustrated. In process, we shall demonstrate the convergence of each of the methods considered. The estimates derived using the ρ-algorithms and ϕ-algorithms are found to be very comparative with other similar type of algorithms.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.08.029