A Note on Generalized Locally Toeplitz Operators

ABSTRACT Generalized Locally Toeplitz (GLT) matrix sequences arise from large linear systems approximating Partial Differential Equations (PDEs), Fractional Differential Equations (FDEs), and Integro‐Differential Equations (IDEs). These sequences are used to study the spectral and singular value behavior of numerical approximations to such equations, achievable via discretization methods like Finite Differences, Finite Elements, Finite Volumes, Isogeometric Analysis, and Discontinuous Galerkin methods. Spectral and singular value symbols are crucial for analyzing eigenvalue and singular value distributions in the Weyl sense. This article offers an operator‐theoretic overview of GLT sequences and explores their use in determining the spectral symbol. Developing an automated procedure for computing these symbols would be beneficial, a task partially addressed by Ahmed Ratnani, N. S. Sarathkumar, and S. Serra‐Capizzano. As an application, we propose an automatic method for computing the symbol of GLT matrix sequences under mild conditions. The spectral symbol , computable through the proposed technique, is not only theoretically significant but also practically valuable for analyzing the convergence of iterative solvers and designing effective preconditioners for ill‐conditioned linear systems.