Analysis of the mean squared derivative cost function
File(s)
Accepted version
Author(s)
Duong, Manh Hong
Tran, Hoang Minh
Type
Journal Article
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.
Date Issued
2017-09-30
Date Acceptance
2017-02-23
Citation
Mathematical Methods in the Applied Sciences, 2017, 40 (14), pp.5222-5240
ISSN
0170-4214
Publisher
Wiley
Start Page
5222
End Page
5240
Journal / Book Title
Mathematical Methods in the Applied Sciences
Volume
40
Issue
14
Copyright Statement
© 2017 John Wiley & Sons, Ltd. This is the accepted version of the following article: Duong, M. H., and Tran, H. M. (2017) Analysis of the mean squared derivative cost function. Math. Meth. Appl. Sci., 40: 5222–5240. doi: 10.1002/mma.4382, which has been published in final form at https://dx.doi.org/10.1002/mma.4382
Identifier
https://doi.org/10.1002/mma.4382
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
mean squared derivative cost functions
variational principle
Wronskian matrix
FOKKER-PLANCK EQUATION
OPTIMAL TRANSPORT
KRAMERS EQUATION
ARM MOVEMENTS
PRINCIPLES
0102 Applied Mathematics
Applied Mathematics
Notes
mrclass: 49K40 (49M25) mrnumber: 3689260
Publication Status
Published
Date Publish Online
2017-04-10