A Ternary Shape-Preserving Refinement Algorithm with Fourth Order Accuracy

Abstract

This paper introduces a new class of stationary refinement algorithms that combine the advantages of the four-point interpolatory algorithm and the cubic B-spline. This algorithm includes a tension parameter. This analysis identifies the range of this parameter and specifies conditions under which the proposed algorithm maintains shape-preserving properties such as monotonicity and convexity. The algorithm achieves improved smoothness, reaching C³ and fourth-order accuracy, while maintaining the same support length as both parent algorithms. Unlike many high-order algorithms that are nonlinear and complex, this method remains simple and efficient. Numerical examples are provided to demonstrate its practical performance, and the proposed algorithm is particularly well-suited for a discontinuous type of data set.