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Rectangular GLT sequences

    Giovanni Barbarino, Carlo Garoni, Mariarosa Mazza, Stefano Serra-Capizzano

ETNA - Electronic Transactions on Numerical Analysis, pp. 585-617, 2022/06/22

doi: 10.1553/etna_vol55s585

doi: 10.1553/etna_vol55s585


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doi:10.1553/etna_vol55s585



doi:10.1553/etna_vol55s585

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.

Keywords: asymptotic distribution of singular values and eigenvalues, rectangular Toeplitz matrices, rectangular generalized locally Toeplitz matrices, discretization of differential equations, finite elements, tensor products, B-splines, multigrid methods