Piecewise linear least squares approximations of Frobenius–Perron operators

We propose a piecewise linear numerical method based on least squares approximations for computing stationary density functions of Frobenius–Perron operators associated with piecewise C2 and stretching mappings of the unit interval. We prove the weak convergence of the method for a class of Frobenius–Perron operators, and the numerical results show that it is also norm convergent and has a better convergence rate than the piecewise linear Markov approximation method.