Comonotone Approximation

The approximation of a piecewise monotonic function f by a polynomial with the same monotonicity. Such comonotonic approximations can always be accomplished with nth degree polynomials, and have an error of Aomega(f;1/n) (Passow and Raymon 1974, Passow et al. 1974, Newman 1979).

This entry contributed by Ronald M. Aarts

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Newman, D. J. "Efficient Co-Monotone Approximation." J. Approx. Th. 25, 189-192, 1979.Passow, E. and Raymon, L. "Monotone and Comonotone Approximation." Proc. Amer. Math. Soc. 42, 340-349, 1974.Passow, E.; Raymon, L.; and Roulier, J. A. "Comonotone Polynomial Approximation." J. Approx. Th. 11, 221-224, 1974.

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Comonotone Approximation

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Aarts, Ronald M. "Comonotone Approximation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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