Aitken sequences and generalized Fibonacci numbers
Authors: J. H. McCabe and G. M. Phillips
Journal: Math. Comp. 45 (1985), 553-558
MSC: Primary 41A21; Secondary 11B39, 65B05
MathSciNet review: 804944
Abstract: Consider the sequence generated by , , where , , with a and b real, of which the Fibonacci sequence is a special case. It is shown that if Aitken acceleration is used on the sequence defined by , the resulting sequence is a subsequence of . Second, if Newton's method and the secant method are used (with suitable starting values) to solve the equation , then the sequences obtained from both of those methods are also subsequences of the original sequence.
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Keywords: Fibonacci sequence, Aitken acceleration, Newton's method, secant method, Padé approximation, continued fraction
Article copyright: © Copyright 1985 American Mathematical Society