基于区域排徐法和方格移动法的矩阵伪谱计算

COMPUTATION OF MATRIX PSEUDOSPECTRA BY EXCLUSION REGIONS AND REMOTION PANE

常用的格子SVD法在精确计算矩阵A的ε-伪谱Λ_ε(A)时,需要将感兴趣的区域作细网格划分,在每一个网格点处计算σ_(min)(zI-A),并根据该值的大小判断该网格点是否位于Λ_ε(A)伪谱曲线上,其计算量往往很大．本文提出两种新的用于计算伪谱的方法:区域排除法和方格移动法．它们以不同方式,减小计算区域,大大提高了伪谱的计算速度．数值实验也充分说明算法的有效性．

The standard grid method （GRID）, which is traditionally used to accurately compute the ε-pseudospectrum ∧ε（A） of a matrix A, is a process of highly demanding computational task. At each point of domain of interest, the GRID computes amin（zI - A） and uses that information in order to classify the point as belonging to ∧ε （A） or not. It means that we shall pay much time for the computation at those points out of the curve. In this paper, we provide two new methods to compute pseudospectra： exclusion regions and remotion pane. They could shrink the regions consumedly and accelerate the speed of computational process. Numerical experiments further show the effectiveness of the methods reported here.