The Norm Convergence of a Least Squares Approximation Method for Random Maps
Raymond Manna Bangura, Congming Jin, Jiu Ding · International Journal of Bifurcation and Chaos · 2021
We prove the [Formula: see text]-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 [Formula: see text]-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.