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Mathematics of Computation

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Anderson-Björck for linear sequences


Author: Richard F. King
Journal: Math. Comp. 41 (1983), 591-596
MSC: Primary 65B99
DOI: https://doi.org/10.1090/S0025-5718-1983-0717729-6
MathSciNet review: 717729
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Abstract: The proposed one-point method for finding the limit of a slowly converging linear sequence features an Anderson-Björck extrapolation step that had previously been applied to the Regula Falsi problem. Convergence is of order 1.839 as compared to $ \sqrt 2 $ for the well-known Aitken-Steffensen $ {\delta ^2}$-process, and to 1.618 for another one-point extrapolation procedure of King. There are examples for computing a polynomial's mutiple root with Newton's method and for finding a fixed point of a nonlinear function.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0717729-6
Keywords: Linear convergence, extrapolation, Aitken's $ {\delta ^2}$-process, Steffensen, Anderson-Björck, efficiency, nonlinear equation, order of convergence, Regula Falsi, linear sequence
Article copyright: © Copyright 1983 American Mathematical Society