The Norm Convergence of a Least Squares Approximation Method for Random Maps

Authors

Raymond Manna Bangura, Zhejiang Sci-Tech University
Congming Jin, Zhejiang Sci-Tech UniversityFollow
Jiu Ding, University of Southern MississippiFollow

Document Type

Article

Publication Date

4-1-2021

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

We prove the L¹-norm and bounded variation norm convergence of a piecewise linear least squares method for the computation of an invariant density of the Foias operator associated with a random map with position dependent probabilities. Then we estimate the convergence rate of this least squares method in the L¹-norm and the bounded variation norm, respectively. The numerical results, which demonstrate a higher order accuracy than the linear spline Markov method, support the theoretical analysis.

Publication Title

International Journal of Bifurcation and Chaos

Volume

31

Issue

5

Recommended Citation

Bangura, R. M., Jin, C., Ding, J. (2021). The Norm Convergence of a Least Squares Approximation Method for Random Maps. International Journal of Bifurcation and Chaos, 31(5).
Available at: https://aquila.usm.edu/fac_pubs/18464