How to extend the application scope of GLT-sequences

In this paper we address the problem of finding the distribution of eigenvalues and singular values for matrix sequences. The main focus of this paper is the spectral distribution for matrix sequences arising in discretization of PDE. In the last two decades the theory of GLT-sequences aimed at this problem has been developed. We investigate the possibility of application of GLT-theory to discretization of PDE on non-rectangular domains and show that in many cases the present GLT-theory is insufficient. We also propose a generalization of GLT-sequences that enables one to cope with a wide range of PDE discretization problems defined on polygonal domains.

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