Here, we consider a more general class of matrix-sequences and we prove that they belong to the maximal $*$-algebra of generalized locally Toeplitz (GLT) matrix-sequences. Then, we identify the associated GLT symbols and GLT momentary symbols in the general setting and in the specific case, by providing in both cases a spectral and singular value analysis. More specifically, we use the GLT tools in order to study the asymptotic behaviour of the eigenvalues and singular values of the considered BDF matrix-sequences, in connection with the given non-uniform grids. Numerical examples, visualizations, and open problems end the present work.

翻译：本文考虑一类更一般的矩阵序列，并证明其属于广义局部Toeplitz（GLT）矩阵序列的最大$*$-代数。随后，我们在一般情形及具体案例中识别了相应的GLT符号与GLT瞬时符号，并针对这两种情形进行了谱分析与奇异值分析。具体而言，我们运用GLT工具研究了所考察的BDF矩阵序列特征值与奇异值的渐近行为，并关联到给定的非均匀网格。数值算例、可视化结果及开放性问题构成了本研究的结尾部分。