  Generalized Locally Toeplitz (GLT) matrix sequences arise from large linear
systems that approximate Partial Differential Equations (PDEs), Fractional
Differential Equations (FDEs), and Integro-Differential Equations (IDEs). GLT
sequences of matrices have been developed to study the spectral/singular value
behaviour of the numerical approximations to various PDEs, Fades and IDEs.
These approximations can be achieved using any discretization method on
appropriate grids through local techniques such as Finite Differences, Finite
Elements, Finite Volumes, Isogeometric Analysis, and Discontinuous Galerkin
methods. Spectral and singular value symbols are essential for analyzing the
eigenvalue and singular value distributions of matrix sequences in the Weyl
sense. In this article, we provide a comprehensive overview of the
operator-theoretic aspect of GLT sequences. The theory of GLT sequences, along
with findings on the asymptotic spectral distribution of perturbed matrix
sequences, is a highly effective and successful method for calculating the
spectral symbol f. Therefore, developing an automatic procedure to compute the
spectral symbols of these matrix sequences would be advantageous, a task that
Ahmed Ratnani, N S Sarathkumar, S. Serra-Capizzano have partially undertaken.
As an application of the theory developed here, we propose an automatic
procedure for computing the symbol of the underlying sequences of matrices,
assuming they form a GLT sequence that meets mild conditions.
