THE QUASI-NEWTON METHOD AND THE INFINITE MATRIX THEORY APPLIED TO THE CONTINUED FRACTIONS

BOUBAKEUR BENAHMED,ALI FARES,BRUNO DE MALAFOSSE

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Abstract

In this paper we first recall some properties of infinite tridiagonal matrices con- sidered as matrix transformations in sequence spaces of the form lp(ξ) and we ex- plicitly 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. AMS Subject Classification: 40C05, 46A15, 90C53.

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Key words

local convergence,continued fraction,linear convergence,leading coefficient,superlinear convergence.,quasi-newton methods,linear system of equations,continued fractions,symmetric rank one method,hilbert space,matrix transformation

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