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.
We use explicit formulas for the mean squared derivative cost function that we obtained in our recent work REF .
Analysis of the mean squared derivative cost function
arXiv: Analysis of PDEs
Mathematics