On the norm convergence of a piecewise linear least squares method for Frobenius–Perron operators

In this paper we prove both the L1-norm and the BV-norm convergence for a piecewise linear least squares approximation method that was recently proposed for computing stationary density functions of Frobenius–Perron operators associated with piecewise C2 and stretching mappings of the unit interval. We also give a convergence rate analysis under the BV-norm.