Least squares data fitting using shape preserving piecewise approximations

In recent years there has been a great deal of interest in the preservation of data properties in an interpolating function, and many good algorithms are available for this problem.In this paper a basis is constructed for a tensioned spline that gives a numerically stable algorithm for theL₂ fitting of data that can preserve monotonicity and/or convexity. The motivation for this work is the fitting of data from a sewerage farm.