Title

Spline monotone approximation with linear differential operators

Abstract

Let f∈C3[a,b] and L be a linear differential operator such that L(f)≥0. Then there exists a sequence Qn, n≥1, of polynomial splines with equally spaced knots, such that Qr, approximates fr, 0≤r≤s, simultaneously in the uniform norm. This approximation is given through inequalities with rates, involving a measure of smoothness to fs; so that L (Qn)≥0. The encountered cases are the continuous, periodic and discrete. © 1989, Springer. All rights reserved.

Publication Title

Approximation Theory and its Applications

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