Speed limit quasi splines and their application to interpolation with bounded first order derivative

Abstract

SummaryThe problem of computing spline‐like functions for ideal data, subject to two‐sided inequality constraints on the first‐order derivative, are considered, focusing primarily on constant constraints and then generalizing. Using a variational approach, in which the inequality constraints are not explicitly imposed, a special type of exponential splines we call speed limit quasi splines is introduced. A simple, non‐parametric, efficient, and robust iterative solver is suggested, which is suitable for a wide range of inequality constraints. Analysis of the convergence factor of this algorithm is provided and supported by extensive numerical tests. Copyright © 2014 John Wiley & Sons, Ltd.