C^2 Tension Splines Construction Based on a Class of Sixth-Order Ordinary Differential Equations

In this work, we construct a class of Hermite-type interpolation basis functions based on the sixth-order ordinary differential equation S^(6)(t) − τ ^4S(2)(t) = 0. Using them, we propose a kind of C^2 tension interpolation splines with a local tension parameter τi. For C^2 interpolation, the given interpolant has O(h^2) convergence. Some applications of the C^2 tension interpolation splines on the construction of interest rate term structure in Chinese financial market are given. Moreover, a kind of generalized non-uniform B-splines of the space spanned by span {1, t, . . . , t^n−4, sin(τ t), cos(τ t), sinh(τ t), cosh(τ t)} is constructed.