We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite the solution of the inverse problem as the solution of a fixed point equation for an affine operator, with linear part satisfying special functional analytical properties. We give a convergence proof for the method and obtain convergence rates for the residual. Convergence rates for the iterates are also obtained under the so called source conditions.

翻译：我们用半组理论重写倒置问题的解决方法,作为线性特殊功能分析特性的固定点方程式的解决方案。 我们为该方法提供趋同证据,并获得剩余物的趋同率。 在所谓的源条件下,迭代国的趋同率也可以获得。