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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1285-1290
  • MSC: Primary 65B99; Secondary 65H05
  • DOI:
  • MathSciNet review: 583505