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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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A characterization theorem for the discrete best monotonic approximation problem
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by I. C. Demetriou PDF
Math. Comp. 55 (1990), 191-195 Request permission


A characterization theorem is derived that motivates a procedure for generating discrete best monotonic approximations to n sequential data values, when a strictly convex objective function is used in the calculation. The procedure is highly useful in the discrete nonlinear optimization calculation that produces the best piecewise monotonic approximations to the data.
  • M. P. Cullinan and M. J. D. Powell, Data smoothing by divided differences, Numerical analysis (Dundee, 1981) Lecture Notes in Math., vol. 912, Springer, Berlin-New York, 1982, pp. 26–37. MR 654340
  • I. C. Demetriou, Data smoothing by piecewise monotonic divided differences, Ph. D. Dissertation, University of Cambridge, 1985.
  • I. C. Demetriou and M. J. D. Powell, Least squares smoothing of univariate data to achieve piecewise monotonicity, IMA J. Numer. Anal. 11 (1991), no. 3, 411–432. MR 1118965, DOI 10.1093/imanum/11.3.411
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 191-195
  • MSC: Primary 65D15
  • DOI:
  • MathSciNet review: 1023046