C2 Tension Splines Construction Based on a Class of Sixth-Order Ordinary Differential Equations

摘要

In this work, we construct a class of Hermite-type interpolation basis functions based on the sixth-order ordinary differential equation S-(6)(t) - tau S-4((2))(t) = 0. Using them, we propose a kind of C-2 tension interpolation splines with a local tension parameter tau(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(tau t), cos(tau t), sinh(tau t), cosh(tau t)} is constructed.

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