Anderson-Björck for linear sequences

King, Richard F.

doi:10.1090/S0025-5718-1983-0717729-6

Anderson-Björck for linear sequences
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Math. Comp. 41 (1983), 591-596 Request permission

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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