The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of square matrices An arising from the discretization of differential problems. Indeed, as the mesh fineness parameter n increases to ∞, the sequence {An}n often turns out to be a GLT sequence. In this paper, motivated by recent applications, we further enhance the GLT apparatus by developing a full theory of rectangular GLT sequences as an extension of the theory of classical square GLT sequences. We also provide two examples of application as an illustration of the potential of the theory presented herein.

Rectangular GLT Sequences

Garoni C.
;
Mazza M.
;
Serra-Capizzano S.
2022-01-01

Abstract

The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of square matrices An arising from the discretization of differential problems. Indeed, as the mesh fineness parameter n increases to ∞, the sequence {An}n often turns out to be a GLT sequence. In this paper, motivated by recent applications, we further enhance the GLT apparatus by developing a full theory of rectangular GLT sequences as an extension of the theory of classical square GLT sequences. We also provide two examples of application as an illustration of the potential of the theory presented herein.
asymptotic distribution of singular values and eigenvalues; B-splines; discretization of differential equations; finite elements; multigrid methods; rectangular generalized locally Toeplitz matrices; rectangular Toeplitz matrices; tensor products
Barbarino, G.; Garoni, C.; Mazza, M.; Serra-Capizzano, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142135
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