Our main contribution in this paper is to present an inexact Matrix-Newton algorithm that uses the tools for Newton's method in Banach spaces to solve a particular type of matrix valued problem: the nonlinear eigenvalue problem with eigenvector dependency (NEPv). We provide the conditions for our algorithm to be applicable to NEPv and show how to exploit the problem structure for an ef- ficient implementation. Various numerical experiments are provided that indicate the advantage of quadratic order of convergence over the linear order of the well- established SCF algorithm.

翻译：本文的主要贡献在于提出了一种不精确矩阵-牛顿算法，该算法利用巴拿赫空间中牛顿方法的工具来求解一类特定的矩阵值问题：特征向量依赖的非线性特征值问题（NEPv）。我们给出了该算法适用于NEPv的条件，并展示了如何利用问题结构进行高效实现。多种数值实验表明，与成熟的SCF算法的线性收敛阶相比，本算法具有二次收敛阶的优势。