Abstract
This chapter discusses the monotone approximation by spline functions. It focuses on the approximation of monotone nondecreasing functions by monotone nondecreasing splines with knots governed by a diffeomorphism. The problem of degree of monotone approximation by polynomials was studied by Lorentz and Zeller. An analogous result in approximation by monotone spline functions with equally spaced knots was obtained by DeVore.
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