Piecewise Linear Least Squares Approximations of Frobenius-Perron Operators

Authors

Jiu Ding, University of Southern MississippiFollow
Noah H. Rhee, University of Missouri, Kansas CityFollow

Document Type

Article

Publication Date

12-1-2010

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

We propose a piecewise linear numerical method based on least squares approximations for computing stationary density functions of Frobenius–Perron operators associated with piecewise C² and stretching mappings of the unit interval. We prove the weak convergence of the method for a class of Frobenius–Perron operators, and the numerical results show that it is also norm convergent and has a better convergence rate than the piecewise linear Markov approximation method.

Publication Title

Applied Mathematics and Computation

Volume

217

Issue

7

First Page

3257

Last Page

3262

Recommended Citation

Ding, J., Rhee, N. H. (2010). Piecewise Linear Least Squares Approximations of Frobenius-Perron Operators. Applied Mathematics and Computation, 217(7), 3257-3262.
Available at: https://aquila.usm.edu/fac_pubs/757