Abstract
The problem of constructing optimal curves for given set of data at discrete data points is considered. Both equally-spaced and non equally-spaced data points are treated. The curves are constituted by using B-splines as basis functions, namely as weighted sum of shifted B-splines of degree k. It is then shown that an optimal approximation can be solved without any boundary conditions, wherein explicit solution formulas are presented. A problem of optimal interpolation is also considered in parallel. Some numerical examples are included to demonstrate the usefulness of the results.
