Radial basis functions are used for fitting a function and its derivatives. The method presented builds on the established orthogonal least squares approach with the additional inclusion of derivative data.

The algorithm is first specified for a function and its derivative, and then extended to incorporate higher order derivatives. Details include the relative weighting of the function and derivatives in the approximation and the creation of enough radial units to accommodate the increased amount of data when derivative values are used.

A good set of references is included for readers interested in background details. Experimental results, limited to first derivative cases, comprise a substantial portion of the paper. An introductory interpolation example shows the significant improvement when derivative data is included, and a longer example involving a set of stability cases in iterated maps. For the extended example, situations illustrating dynamical system behavior from equilibrium to chaos are studied. The paper is well organized, with clear definitions of terms and algorithm descriptions, well-used graphics in the examples, and supporting linear algebra detail deferred to an appendix.