Future Developments

Carlo Garoni () and Stefano Serra-Capizzano ()
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Carlo Garoni: University of Insubria, Department of Science and High Technology
Stefano Serra-Capizzano: University of Insubria, Department of Science and High Technology

Chapter Chapter 11 in Generalized Locally Toeplitz Sequences: Theory and Applications, 2017, pp 261-263 from Springer

Abstract: Abstract As explainedUnilevel GLT sequence Univariate GLT sequence in the preface, the present Volume I developed the theory of univariate (or unilevel) GLT sequences (though for simplicity we everywhere dropped the adjective univariate/unilevel). This is the reason why the applications of Sects. 10.5 – 10.7 only addressed the discretization of unidimensional DEs. Volume II [64] will take care of developing the theory of multivariate (multilevel) GLT sequences and will present the correspondingMultilevel GLT sequence Multivariate GLT sequence applications to the discretization of multidimensional DEs (i.e., PDEs). After Volume II, further volumes will be necessary to develop the theory of multilevel block and reduced GLT sequences. Here we formally state these and other possible future developments, which may also be regarded as future lines of research, since the theory of block and reduced GLT sequences still needs to be revised, extended and organized in a systematic way.

Keywords: Unilevel; Multilevel Block; Toeplitz Sequences; Singular Value Distribution; Constant Coefficient PDE (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-53679-8_11

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