论文标题
通过GLT瞬时符号对矩阵序列的光谱分析的注释：从抛物线问题的全面解决方案到分布的分数级矩阵
A note on the spectral analysis of matrix sequences via GLT momentary symbols: from all-at-once solution of parabolic problems to distributed fractional order matrices
论文作者
论文摘要
本文的第一个焦点是频谱的表征和系数矩阵的奇异值是由抛物线扩散问题的离散化和时空网格引起的，以及分布式阶分数方程的近似值。为此，我们将使用经典的GLT理论和GLT瞬时符号的新概念。第一个允许描述系数矩阵序列的奇异值或特征值渐近分布，后者允许得出一个函数，该函数描述了序列矩阵的奇异值或特征值分布，即使对于小矩阵大小，但在给定假设下也是如此。该注释以开放问题的列表结束，包括在迭代矩阵研究中使用我们的机械，尤其是与跨越型技术有关的矩阵。
The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization with space-time grid for a parabolic diffusion problem and from the approximation of distributed order fractional equations. For this purpose we will use the classical GLT theory and the new concept of GLT momentary symbols. The first permits to describe the singular value or eigenvalue asymptotic distribution of the sequence of the coefficient matrices, the latter permits to derive a function, which describes the singular value or eigenvalue distribution of the matrix of the sequence, even for small matrix-sizes but under given assumptions. The note is concluded with a list of open problems, including the use of our machinery in the study of iteration matrices, especially those concerning multigrid-type techniques.
