Smoothness beyond Differentiability
نویسنده
چکیده
The traditional concept of smoothness concerns differentiability, and we consider a function to be smooth if it is k-times differentiable. This concept is important in many aspects of numerical analysis, and the quality of reconstructions of signals from certain given observations depend on this information. For instance, a k-times differentiable function on the unit cube [0, 1] can be approximated by certain splines at the order n−k/d, where n denotes the number of information (values at a grid). In inverse problems, when we are given data
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