Spline Toolbox

Example: Approximation by Tensor Product Splines

Since the toolbox can handle splines with vector coefficients, it is easy to implement interpolation or approximation to gridded data by tensor product splines, as the following illustration, run by tspdem, is meant to show.

To be sure, most tensor product spline approximation to gridded data can be obtained directly with one of the spline construction commands, like spapi or csape, in this toolbox, without concern for the details discussed in this example. Rather, this example is meant to illustrate the theory behind the tensor product construction, and this will be of help in situations not covered by the construction commands in this toolbox.

This section discusses these aspects of the tensor product spline problem:

• Choice of Sites and Knots
• Least Squares Approximation as Function of y
• Approximation to Coefficients as Functions of x
• It provides the bivariate spline approximation
• Switch in Order
• Approximation to Coefficients as Functions of y
• The Bivariate Approximation
• Comparison and Extension

Remez Iteration

Choice of Sites and Knots