On infinite series representations of real numbers

János Galambos

Displaying similar documents to “On infinite series representations of real numbers”

An analysis of selection sort using recurrence relations.

Francesc J. Ferri, Jesús Albert (1996)

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This paper presents a method for obtaining the expected number of data movements executed by the well-known Selection sort algorithm along with its corresponding variance. The approach presented here requires hardly any specific mathematical background. In particular, the average-case cost and variance are represented using recurrence relations whose solutions lead to the desired results. Even though this method is not applicable in general, it serves to conveniently present average-case...

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Some results on convergence acceleration for the E-algorithm

A. Fdil (1997)

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Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments

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Jan Ježek (1988)

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The paper is devoted to an algorithm for computing matrices $A^{r}$ and $(A^{r} - I) . {(A - I)}^{- 1}$ for a given square matrix $A$ and a real $r$ . The algorithm uses the binary expansion of $r$ and has the logarithmic computational complexity with respect to $r$ . The problem stems from the control theory.

Convergence acceleration by the $E_{+ p}$ -algorithm

A. Fdil (1998)

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A new algorithm which generalizes the E-algorithm is presented. It is called the $E_{+ p}$ -algorithm. Some results on convergence acceleration for the $E_{+ p}$ -algorithm are proved. Some applications are given.