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 τ _i . 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.