Bivariate free knot splines (Q1397989)

The nonlinear approximation problem of spline approximation with free knots is considered and extended to two dimensions. To this end, tensor product methods are used to generalise univariate spline to bivariate ones. Further, the approximation problem is based on minimising a standard functional of square integrals of second partial derivatives in two dimensions (sometimes called thin-plate spline functional or Duchon or Schoenberg functional). Several numerical methods and examples are provided as well.