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.

中文翻译：

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随机映射最小二乘逼近法的范数收敛

我们证明大号1-范数和有界变化范数收敛分段线性最小二乘法用于计算与具有位置相关概率的随机地图相关联的 Foias 算子的不变密度。然后我们估计这种最小二乘法的收敛速度大号1-范数和有界变化范数，分别。数值结果表明比线性样条马尔可夫方法具有更高的阶精度，支持理论分析。