Spline Approximation Using Knot Density Functions

This paper, resulting from research collaboration with the UK National Physical Laboratory, is the first to present successfully a simple method for controlling the location parameters in univariate spline approximations. Traditional highly non-linear approaches are avoided by considering the parameters to be a function of a given density model. We present a number of density models for a range of data types, such as dominant local variability. This paper delivers to a scientific discipline applying polynomial spline approximations to recover discrete data to a high level of accuracy a method which avoids the need to construct complicated mathematical models.