AndersonBjörck for linear sequences
Author:
Richard F. King
Journal:
Math. Comp. 41 (1983), 591596
MSC:
Primary 65B99
MathSciNet review:
717729
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Abstract: The proposed onepoint method for finding the limit of a slowly converging linear sequence features an AndersonBjörck extrapolation step that had previously been applied to the Regula Falsi problem. Convergence is of order 1.839 as compared to for the wellknown AitkenSteffensen process, and to 1.618 for another onepoint 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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 R. F. King, "An extrapolation method of order four for linear sequences," SIAM J. Numer. Anal., v. 16, 1979, pp. 719725. MR 543964 (80f:65051)
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 R. F. King, "An efficient onepoint extrapolation method for linear convergence," Math. Comp., v. 35, 1980, pp. 12851290. MR 583505 (82b:65004)
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 D. E. Muller, "A method for solving algebraic equations using an automatic computer," Math. Comp., v. 10, 1956, pp. 208215. MR 0083822 (18:766e)
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 J. F. Steffensen, "Remarks on iteration," Skandinavisk Aktuarietidskrift, v. 16, 1933, pp. 6472.
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 J. F. Traub, Iterative Methods for the Solution of Equations, PrenticeHall, Englewood Cliffs, N. J., 1964. MR 0169356 (29:6607)
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 H. Van de Vel, "A method for computing a root of a single nonlinear equation, including its multiplicity," Computing, v. 14, 1975, pp. 167171. MR 0403205 (53:7017)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198307177296
PII:
S 00255718(1983)07177296
Keywords:
Linear convergence,
extrapolation,
Aitken's process,
Steffensen,
AndersonBjörck,
efficiency,
nonlinear equation,
order of convergence,
Regula Falsi,
linear sequence
Article copyright:
© Copyright 1983
American Mathematical Society
