\(C^ 1\) splines for interpolation of rapidly varying data (Q801230)

C\({}^ 2\)-spline interpolants to rapidly varying data tend to be unreasonably oscillatory. By requiring the piecewise cubic interpolant to minimize a weighted, rather than unweighted \(L_ 2\)-norm of the second derivative, the oscillations can be reduced at the cost of order of differentiability. In particular, it is shown how a weight function which depends on the data can be usefully employed. An example of interpolation to bivariate data by blending profiles which are constructed by weighted spline interpolation is given.