Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 31, Issue 5, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127421500681
Keywords
Random map; absolutely continuous invariant measure; stationary density; least squares; Frobenius-Perron operator; Foias operator
Funding
- National Science Foundation of China [11571314]
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The study proves the 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, in L1-norm and bounded variation norm. The convergence rate of this method is estimated in both norms. Numerical results indicate higher accuracy compared to the linear spline Markov method, supporting the theoretical analysis.
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.
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