关于对角占优矩阵的几点教学注记

Several Teaching Notes on Diagonally Dominant Matrices

摘要: 本文针对对角占优矩阵的教学提出了一些注记。首先，根据对角占优矩阵的可逆性和圆盘定理的证明过程的相似性，我们提出了相应的教学注记。此外，讨论了对角占优矩阵Jacobi和Gauss-Seidel迭代法的收敛性分析，并基于定理的证明过程分析了该两类迭代法的异同性，从而给出相关教学注记。

Abstract: This paper puts forward some notes on the teaching of diagonally dominant matrices. First, employing the similarity of proof process for the invertibility of diagonally dominant matrices and the disk theorem, we provide the corresponding teaching notes. Additionally, the convergence analysis of Jacobi and Gauss-Seidel iterative methods on the diagonally dominant matrices is discussed. Based on the proof process of the theorems, the similarities and differences between these two types iterative methods are also analyzed; thereby the relevant teaching notes are given.