Comonotone Approximation

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).

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.