论文标题
在多项式时间内解决$ p $ laplacian的有效算法
Efficient algorithms for solving the $p$-Laplacian in polynomial time
论文作者
论文摘要
$ p $ -laplacian是一个非线性偏微分方程，由$ p \ in [1，\ infty] $进行了参数。我们根据障碍法提供了新的数值算法，用于以$ o（\ sqrt {n} \ log n）$ o（\ sqrt {n} \ log n）$ newton Iterations in [1，\ infty] $中的所有$ p \ newton迭代求解$ p $ -laplacian，其中$ n $ n $ n $ n $ n $是网格点的数量。我们通过数值实验确认我们的估计值。
The $p$-Laplacian is a nonlinear partial differential equation, parametrized by $p \in [1,\infty]$. We provide new numerical algorithms, based on the barrier method, for solving the $p$-Laplacian numerically in $O(\sqrt{n}\log n)$ Newton iterations for all $p \in [1,\infty]$, where $n$ is the number of grid points. We confirm our estimates with numerical experiments.
