THEORY OF EXPONENTIAL SPLINES

Pruess [12, 14] has shown that exponential splines can produce co-convex and co-monotone interpolants. These results justify the further study of the mathematical properties of exponential splines as they pertain to their utility as numerical approximations. They also warrant the generalization of the exponential spline in fruitful directions. Herein, we present convergence rates and extremal properties for exponential spline approximation, cardinal spline and B-spline bases for the space of exponential splines, and generalizations to higher order tension splines and Hermite tension interpolants. © 1991.