Least-Squares Approximation Method For Random Maps

Several approximation methods have been employed in the computation of stationary density functions of random maps.Here,we proved the L1-norm,and bounded variation norm(BV-norm)convergence of a piecewise linear least-squares method for the computation of the invariant density for random maps with position-dependent probabilities.Also,we gave the convergence rate of the least-squares method in the L1-norm and the BV-norm,each.Finally,we showed that the numerical results of a piecewise linear leastsquares method has a higher-order accuracy than the linear spline Markov method from the theoretical analysis.