Exponential Term in Spline Polynomial

Question

Need some help here.

A cubic spline takes the form of:

$a + b^t + ct^2 + dt^3$

Is there such a spline that incorporates an exponential term to take the form of:

$a + bt + ct^2 + dt^3 + fe^{Xt}$

where $X$ is just some constant?

Thanks!

Grant

Answer 1

There are some "spline under tension" curves that use exponential functions (hyperbolic sines and cosines, actually). They don't have exactly the form you described. When the tension parameter is set to zero, they reduce to conventional cubic splines. They are not widely used. Here is one reference. You'll find others if you search for "spline under tension".