Study Of Cubic Spline Interpolation In Power Exponent Form

Interpolating function in power exponent form is a new research filed for approximating function in recent years, Which changes the form of interpolating function in polynomial to in exponential by the speciality of (?)xponential function. It is a kind of generalization of function interpolating. We can see researches in this area in some scientific journal.In virtue of the mathematic theories and conformation mechanism about interpolation , this paper comes up with a new concept of cubic spline interpolation in power exponent form, based on studying on the theories of spline interpolation and the characteristic of interpolating function in power exponential . Furthermore, aiming at three different kinds of boundaries, this paper offers evidence for the existence and uniqueness of cubic spline interpolation in power exponent form when node is isometric node, and the restrictive conditions when node is not isometric node.Comparing with existed spline interpolation in power exponent form, this new cubic spline interpolation in power exponent form is applicable in more wide range and can receive more results. The computation indicates that new-style cubic spline interpolation in power exponent form can effectively solve any problems that can be solved by cubic spline interpolation, which can approximate original function better and achieve the target of enhancing computational efficiency.Moreover, cubic spline interpolation will be complex in computation on some problems, this new-style cubic spline interpolation in power exponent form can predigest computation and improve computational efficiency to an extent.