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Discrete mollification and automatic numerical differentiation. (English) Zbl 0910.65010

Numerical differentiation is an unreliable procedure in the case of a function with noise. The authors continue the study of their proposal to remedy this by a mollification procedure. This is based on the idea of replacing the given function by a convolution product with a smooth function of a given type with small support. This leads to an automatic method for numerical differentiation based on discrete mollification. With data measured at a discrete set of points, the method allows the approximate recovery of the derivative function in all points of the interval. The authors prove rigorous error bounds and present several interesting numerical examples.
Reviewer: W.Govaerts (Gent)

MSC:

65D25 Numerical differentiation
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