Rectangular GLT Sequences
Carlo Garoni, Giovanni Barbarino, Mariarosa Mazza, Stefano Serra‐Capizzano
2022Oesterreichisches Musiklexikon online (Institut für kunst- und musikhistorische Forschungen der Österreichischen Akademie der Wissenschaften)12 citationsDOIOpen Access PDF
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.
Topics & Concepts
Toeplitz matrixMathematicsDiscretizationSequence (biology)Extension (predicate logic)Square (algebra)Pure mathematicsApplied mathematicsMathematical analysisGeometryComputer scienceProgramming languageGeneticsBiologyMatrix Theory and AlgorithmsHolomorphic and Operator TheoryAdvanced Topics in Algebra