论文标题
通过离散化伪造
Pseudospectrum enclosures by discretization
论文作者
论文摘要
提出了一种通过矩阵或线性运算符的数值范围包围伪谱的新方法。该方法应用于无限维二维Hilbert空间上操作员的有限维离散，并获得了不同近似方案的收敛结果，包括有限元方法。我们表明，完整运算符的伪谱包含在集合的交集中，这些集合以近似矩阵的移位倒置的数值范围表示。通过两个例子说明了结果：对流扩散操作员和Hain-Lüst操作员。
A new method to enclose the pseudospectrum via the numerical range of the inverse of a matrix or linear operator is presented. The method is applied to finite-dimensional discretizations of an operator on an infinite-dimensional Hilbert space, and convergence results for different approximation schemes are obtained, including finite element methods. We show that the pseudospectrum of the full operator is contained in an intersection of sets which are expressed in terms of the numerical ranges of shifted inverses of the approximating matrices. The results are illustrated by means of two examples: the advection-diffusion operator and the Hain-Lüst operator.
