动力学系统伪谱与扰动系统谱的关系

Relationships of Pseudo-spectra of Dynamis Systems with Spectra of Its Perturbed Systems

波形松弛算子通常是高度非正规的。这时 ,采用传统的谱概念来研究算子和迭代法的特性就会遇到困难。利用常微分方程系统波形松弛算子的伪谱 ,证明扰动系统波形松弛算子的谱是矩阵束伪谱 ,并给出扰动系统的谱通常包含在未扰动系统的伪谱中 ,从而进一步证实了在非正规系统中伪谱确实是一个有用的科学计算工具。

The waveform relaxation operator for many problems tends to be highly nonnormal,because the spectrum is not a good predictor of the behavior of the operator.The pseudo-spectra of waveform relaxation operators for ordinary differential equation systems are used,the spectra of perturbed systems are proved to be pseu-dospectra of matrix pencils.An inclusion relationship between them is obtained. The work here further confirms that the concept of pseu-dospectra is really a useful tool in scientific computation for nonnormal systems.