A unified maximum entropy method via spline functions for Frobenius-Perron operators

Jiu Ding; Noah H. Rhee

doi:10.3934/naco.2013.3.235

Article Contents

2013, Volume 3, Issue 2: 235-245. Doi: 10.3934/naco.2013.3.235

This issue Previous Article Subspace trust-region algorithm with conic model for unconstrained optimization Next Article Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming

A unified maximum entropy method via spline functions for Frobenius-Perron operators

Jiu Ding^1, and
Noah H. Rhee^2,

1.
Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406-5045
2.
Department of mathematics and Statistics, The University of Missouri - Kansas City, Kansas City, MO 64110-2499

Received: February 2012

Revised: January 2013

Published: April 2013

Abstract / Introduction Related Papers Cited by

Abstract

We present a general frame of finite element maximum entropy methods for the computation of a stationary density of Frobenius-Perron operators associated with one dimensional transformations, based on spline function approximations. This gives a unified numerical approach to the density recovery for this class of positive operators by combining the principle of maximum entropy with the idea of finite elements. The norm convergence of the method is proved and the numerical results with the piecewise cubic method show its fast convergence.

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Mathematics Subject Classification: Primary: 41A35, 65D07; Secondary: 65J10.

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