In this paper we introduce and analyze an iteratively re-weighted algorithm, that allows to approximate the weak solution of the p-Poisson problem for $$1 < p \leqslant 2$$ by iteratively solving a sequence of linear elliptic problems. The algorithm can be interpreted as a relaxed Kacanov iteration, as so-called in the specific literature of the numerical solution of quasi-linear equations. The main contribution of the paper is proving that the algorithm converges at least with an algebraic rate.

中文翻译：

---

p-泊松问题的松弛 Kačanov 迭代

在本文中，我们介绍并分析了一种迭代重加权算法，该算法允许通过迭代求解一系列线性椭圆问题来逼近 $$1 < p \leqslant 2$$ 的 p-Poisson 问题的弱解。该算法可以解释为松弛的 Kacanov 迭代，正如在拟线性方程的数值解的特定文献中所称的那样。该论文的主要贡献是证明该算法至少以代数率收敛。