论文标题
用于计算非线性操作员特征向量的迭代方法
Iterative Methods for Computing Eigenvectors of Nonlinear Operators
论文作者
论文摘要
在本章中，我们正在研究解决非线性特征值问题的几种迭代方法。这些出现在各种图像处理，图形分区和分类，非线性物理学等。我们解决的规范本本特征是$ t（u）=λu$，其中$ t：\ r^n \ to \ r^n $是一些有界的非线性操作员。还讨论了特征值问题的其他变化。我们提出了5种算法的进展，近年来作者及其同事共同撰写。每种算法都试图解决一个独特的问题或改善理论基础。可以将算法理解为非线性PDE的算法，该算法会收敛到连续的时域中的特征功能。这允许对离散迭代过程的独特视图和理解。最后，它显示了如何以数值评估结果，以及一些与非线性Deoisers先验有关的示例和见解，包括经典算法和基于深网络的算法。
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we solve is $T(u)=λu$, where $T:\R^n\to \R^n$ is some bounded nonlinear operator. Other variations of eigenvalue problems are also discussed. We present a progression of 5 algorithms, coauthored in recent years by the author and colleagues. Each algorithm attempts to solve a unique problem or to improve the theoretical foundations. The algorithms can be understood as nonlinear PDE's which converge to an eigenfunction in the continuous time domain. This allows a unique view and understanding of the discrete iterative process. Finally, it is shown how to evaluate numerically the results, along with some examples and insights related to priors of nonlinear denoisers, both classical algorithms and ones based on deep networks.
