Spline monotone approximation with linear differential operators
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.
Approximation Theory and its Applications
Anastassiou, G. (1989). Spline monotone approximation with linear differential operators. Approximation Theory and its Applications, 5 (4), 61-67. https://doi.org/10.1007/BF02836070