A Newton Method for Shape-Preserving Spline Interpolation

Abstract. In 1986, Irvine, Marin, and Smith proposed a Newton-type method for shapepreserving interpolation and, based on numerical experience, conjectured its quadratic convergence. In this paper, we prove local quadratic convergence of their method by viewing it as a semismooth Newton method. We also present a modification of the method which has global quadratic convergence. Numerical examples illustrate the results.