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The Quasi-Newton Method and the Infinite Matrix Theory Applied to the Continued Fractions

Volume 8, Number 2 (2009), 1 - 16

The Quasi-Newton Method and the Infinite Matrix Theory Applied to the Continued Fractions

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Abstract

In this paper we first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the form lp (x) and we explicitly calculate the leading coefficient of an Az-fraction in special cases. Then in more general cases we use the quasi-Newton method where we explicit a sequence that converges fast to the leading coefficient of a continued fraction.