Monotonicity of some perturbations of irreducibly diagonally dominant M-matrices
Monotonicity of some perturbations of irreducibly diagonally dominant M-matrices
复制标题
不可约对角占优M矩阵的一些扰动的单调性
作者：
F. Bouchon
本文提出了有关M-矩阵微扰理论的新结果。我们给出了一个定理的证明，该定理表明不可约对角占优 M 矩阵的某些扰动是单调的，并且具有扰动范数的显式界限。关于扰动矩阵的假设之一是其每一行的条目之和是非负的。结果矩阵显示为单调，尽管它可能不是对角占优的，并且其非对角部分可能有一些正项。作为应用，我们给出了应用于椭圆边值问题的非中心有限差分格式的二阶收敛性的证明。
This paper presents a new result concerning the perturbation theory of M-matrices. We give the proof of a theorem showing that some perturbations of irreducibly diagonally dominant M-matrices are monotone, together with an explicit bound of the norm of the perturbation. One of the assumptions concerning the perturbation matrix is that the sum of the entries of each of its row is nonnegative. The resulting matrix is shown to be monotone, although it may not be diagonally dominant and its off diagonal part may have some positive entries. We give as an application the proof of the second order convergence of an non-centered finite difference scheme applied to an elliptic boundary value problem.