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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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Optimal numerical differentiation using three function evaluations
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by J. Marshall Ash and Roger L. Jones PDF
Math. Comp. 37 (1981), 159-167 Request permission

Abstract:

Approximation of $f’ (x)$ by a difference quotient of the form \[ {h^{ - 1}}[{a_1}f(x + {b_1}h) + {a_2}f(x + {b_2}h) + {a_3}f(x + {b_3}h)]\] is found to be optimized for a wide class of real-valued functions by the surprisingly asymmetric choice of ${\mathbf {b}} = ({b_1},{b_2},{b_3}) = (1/\sqrt 3 - 1,1/\sqrt 3 ,1/\sqrt 3 + 1)$. The nearly optimal choice of ${\mathbf {b}} = ( - 2,3,6)$ is also discussed.
References
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 159-167
  • MSC: Primary 65D05; Secondary 39A05
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0616368-3
  • MathSciNet review: 616368