A Piecewise Quadratic Maximum Entropy Method for the Statistical Study of Chaos
Document Type
Article
Publication Date
1-15-2015
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
Let the Frobenius–Perron operatorPS:L1(0,1)→L1(0,1), related to a nonsingular transformationS:[0,1]→[0,1], have an invariant densityf⁎. We propose a piecewise quadratic maximum entropy method for the numerical approximation off⁎. The role of the partition of unity property of the quadratic functions for the numerical recovery off⁎has been depicted. The proposed algorithm overcomes the ill-conditioning shortage of the traditional maximum entropy method which only employs polynomials, so that any number of moments can be used to increase the accuracy of the computed invariant density. The convergence rate of the method is shown to be of order 3. Numerical results are presented to justify the theoretical analysis of the method.
Publication Title
Journal of Mathematical Analysis and Applications
Volume
421
Issue
2
First Page
1487
Last Page
1501
Recommended Citation
Upadhyay, T.,
Ding, J.,
Rhee, N. H.
(2015). A Piecewise Quadratic Maximum Entropy Method for the Statistical Study of Chaos. Journal of Mathematical Analysis and Applications, 421(2), 1487-1501.
Available at: https://aquila.usm.edu/fac_pubs/15275