On a Descent Algorithm for the Discrete Best Linear Spline Approximation Problem

Let there be given error-contaminated measurements of function values at strictly ascending abscissae. We address the problem of calculating a best linear spline approximation to these data, whose knots are predefined on the abscissae. We establish conditions that allow the development of a special descent algorithm that takes into account the structure of the problem. 1 Index Terms data fitting, divided difference, approximation, least absolute deviation, linear programming, smoothing, spline 1