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 | References | Similar Articles | Additional Information

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 for the well-known Aitken-Steffensen -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 -process,
Steffensen,
Anderson-Björck,
efficiency,
nonlinear equation,
order of convergence,
Regula Falsi,
linear sequence

Article copyright:
© Copyright 1983
American Mathematical Society