Abstract. The concept of modification used for accelerating the convergence of ordinary continued... more Abstract. The concept of modification used for accelerating the convergence of ordinary continued fractions is adapted to the case of the Gautschi-Aggarwal-Burgmeier algorithm for the computation of nondominant solutions of nonhomogeneous second-order linear recurrence relations. Key words, convergence acceleration, recurrence relation, continued fraction AMS(MOS) subject classifications. 65Q05, 65B99, 40A15 1. Introduction. One
In this paper we presenta new modificationof a generalized continuedfractionor n-fractionfor whic... more In this paper we presenta new modificationof a generalized continuedfractionor n-fractionfor whichtheunderlyingrecurrence relationis of Perron-Kreusertype.If thecharacteristicequationsfor this recurrencerelationhaveonlysimplerootswith differingabsolute values.thenthisnewmodificationleadstoconvergenceacceleration. 1. Introductionandnotation In a previous paper [2] we defineda modificationof a convergentn-fraction associated with a recurrencerelation of Perron-Kreusertype. This modificationoften leadsto conver-genceacceleration.One of the disadvantagesof the methodgiven in [2] is that it requires the calculation of the roots of a certainpolynomial equation.In this paper we presenta
In this note we relate two methods of convergence acceleration for ordinary continued fractions, ... more In this note we relate two methods of convergence acceleration for ordinary continued fractions, the first one is due to Lorentzen and Waadeland [1, 2], the second one to Waadeland [7, 8, 9, 10, 11]. Keywords: Continued fractions, convergence acceleration. AMS Classification: 40A15, 65B99, 65Q05
We present here two classes of infinite series and the associated continued fractions involving $... more We present here two classes of infinite series and the associated continued fractions involving $\pi$ and Catalan's constant $G$ based on the work of Euler and Ramanujan. A few sundry continued fractions are also given.
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Papers by Paul Levrie