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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An efficient one-point extrapolation method for linear convergence
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by Richard F. King PDF
Math. Comp. 35 (1980), 1285-1290 Request permission

Abstract:

For iteration sequences otherwise converging linearly, the proposed one-point extrapolation method attains a convergence rate and efficiency of 1.618. This is accomplished by retaining an estimate of the linear coefficient from the previous step and using the estimate to extrapolate. For linear convergence problems, the classical Aitken-Steffensen ${\delta ^2}$-process has an efficiency of just $\sqrt 2$, while a recently proposed fourth-order method reaches an efficiency of 1.587. Not only is the method presented here more efficient, but it is also quite straightforward. Examples given are for Newton’s method in finding multiple polynomial roots and for locating a fixed point of a nonlinear function.
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1285-1290
  • MSC: Primary 65B99; Secondary 65H05
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583505-8
  • MathSciNet review: 583505