Analysis of the mean squared derivative cost function

TL;DR

This paper studies mean squared derivative cost functions, providing analytical formulas, computational algorithms, and numerical simulations, while also deriving an explicit inverse for a Wronskian matrix of independent interest.

Contribution

It offers new explicit formulas, algorithms, and insights into mean squared derivative costs, including a novel inverse Wronskian matrix formula.

Findings

Derived explicit formulas for cost functions

Developed computational algorithms for evaluation

Numerical simulations confirmed analytical results

Abstract

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by-product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory.