A method for computing the tension parameters in convexitity-preserving spline-in-tension interpolation (Q1098223)

This paper is concerned with the problem of convexity-preserving (or c- preserving) interpolation by using exponential splines in tension (or EST's). For this purpose the notion of a c-preserving interpolant, which is usually employed in spline-in-tension interpolation, is refined and the existence of c-preserving EST's is established for the so-called c- admissible data sets. The problem of constructing a c-preserving and visually pleasing EST is then treated by combining a generalized Newton- Raphson method, due to Ben-Israel, with a step-length technique which serves the need for ``visual pleasantness''. The numerical performance of the so formed iterative scheme is discussed for several examples.