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.

中文翻译：

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离散化的伪谱附件

提出了一种通过矩阵或线性算子的逆数值范围包围伪光谱的新方法。该方法应用于无穷维希尔伯特空间上算子的有限维离散化，并获得了包括有限元方法在内的不同近似方案的收敛结果。我们表明，全算子的伪谱包含在集合的交集中，这些交集以近似矩阵的移位逆的数值范围表示。通过两个示例说明了结果：对流扩散算子和Hain-Lüst算子。