发表机构
University of Sfax; University of Wuppertal; Technische Universität Ilmenau（萨法克斯大学; 伍珀塔尔大学; 伊尔梅瑙工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过值域表示将块数值域从算子推广到线性关系，所得块数值域可能非凸，能检测谱间隙，并应用于端口哈密顿DAEs获得左半平面谱界。
AI 中文摘要
线性关系是线性算子的多值推广，其谱性质与微分代数方程的稳定性密切相关。因此，可靠的谱包含集具有相当大的研究意义。在本文中，我们通过值域表示将块数值域的既有概念从算子推广到线性关系。与经典数值域不同，所得的块数值域可能非凸，因而能够检测谱中的间隙。我们建立了这一新概念的基本性质，并推导了相应的谱包含结果。最后，我们通过一个数值示例比较了由不同构造得到的块数值域，以说明该理论。作为应用，我们为一类端口哈密顿微分代数方程获得了显式的左半平面谱界。
英文摘要
Linear relations are multivalued generalizations of linear operators whose spectral properties are closely linked to the stability of differential-algebraic equations. Consequently, reliable spectral enclosures are of considerable interest. In this note, we extend the established concept of the block numerical range from operators to linear relations by means of a range representation. Unlike the classical numerical range, the resulting block numerical range may be nonconvex and can therefore detect gaps in the spectrum. We establish fundamental properties of this new notion and derive corresponding spectral enclosure results. Finally, we illustrate the theory with a numerical example comparing the block numerical ranges obtained from different constructions. As an application, we obtain an explicit left-half-plane spectral bound for a class of port-Hamiltonian DAEs.
Comments21 pages, 4 figures
