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Tight Smoothing of Singular Functions
- The present operator performs a tight smoothing on the input function. Let ƒ be a scalar function of any number of variables, which can be not continuous or nor smooth, that is,
ƒ can be continuous but not continuously differentiable, the smoothing operator
when applied to ƒ will return a smooth function which is equal to the input function
ƒ apart from a neighborhood of the singularities of ƒ. The width of the neighbourhood is controlled by a parameter l. The larger is
l, the smaller is the neighborhood. For l → +∞, Slƒ
→ ƒ, whereas for l → 0, Slƒ → co(ƒ), convex envelope of ƒ.