The approximation of a piecewise monotonic function 
by a polynomial with the same monotonicity. Such comonotonic approximations can always
be accomplished with 
th degree polynomials, and have an error of 
(Passow and Raymon 1974, Passow et al. 1974,
Newman 1979).
Comonotone Approximation
This entry contributed by Ronald M. Aarts
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References
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.Referenced on Wolfram|Alpha
Comonotone ApproximationCite this as:
Aarts, Ronald M. "Comonotone Approximation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ComonotoneApproximation.html