The not-a-knot piecewise interpolatory cubic polynomial

摘要

In this paper, the main idea of the not-a-knot cubic spline of De Boor [8] will be extended to all the interior points (knots) of the spline interval to obtain a piecewise interpolatory cubic polynomial. Instead of the original and conventional not-a-knot cubic spline, to construct this piecewise polynomial we do not need to solve a tridiagonal system of linear equations, and this provides a shortcut which helps us save the time of doing more computations. The order of convergence of this piecewise cubic polynomial is O(h4).