Computation of Exponential Splines

Pruess’s investigations [J. Approx. Theory, 17 (1976), pp. 86–96], [Math. Comp., 33 (1979), pp. 1273–128 1] revealed the shape preservation properties of exponential splines and provided the impetus for further theoretical study of exponential splines [J. Approx. Theory, to appear]. Together, these theoretical results form the backdrop for the detailed analysis of issues in the computation of exponential splines contained herewith. Specifically, first and foremost the construction of tension parameter selection algorithms is considered. The conditioning and iterative solution of the spline equations, as well as the derivation and accuracy of end conditions, are discussed. This inquiry concludes with a potpourri of numerical considerations and the presentation of a variety of numerical examples.