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Sbornik: Mathematics, 2017, Volume 208, Issue 11, Pages 1602–1627
DOI: https://doi.org/10.1070/SM8823 (Mi sm8823) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey

A. Böttchera, C. Garonibc, S. Serra-Capizzanobd

a Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany
b Department of Science and High Technology, University of Insubria, Como, Italy
c Institute of Computational Science, Università della Svizzera Italiana, Lugano, Switzerland
d Department of Information Technology, Uppsala University, Uppsala, Sweden
English version PDF (707 kB) Citations (14)
References:
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DOI: https://doi.org/10.1070/SM8823
Abstract: It is often asked why Toeplitz-like matrices with unbounded symbols are worth studying. This paper gives an answer by presenting several concrete problems that motivate such studies. It surveys the central results of the theory of Generalized Locally Toeplitz (GLT) sequences in a self-contained tool-kit fashion, and gives a new extension from bounded Riemann integrable functions to unbounded almost everywhere continuous functions. The emergence of unbounded symbols is illustrated by local grid refinements in finite difference and finite element discretizations and also by preconditioning strategies.
Bibliography: 40 titles.
Keywords: Toeplitz-like matrices, eigenvalue distribution, singular value distribution, GLT-sequences, local grid refinement.
Funding agency Grant number
Istituto Nazionale di Alta Matematica "Francesco Severi" PCOFUND-GA-2012-600198
Carlo Garoni is a Marie-Curie fellow of the Italian INdAM (Istituto Nazionale di Alta Matematica “Francesco Severi”) under grant agreement PCOFUND-GA-2012-600198).
Received: 02.07.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 11, Pages 29–55
DOI: https://doi.org/10.4213/sm8823
Bibliographic databases:
Document Type: Article
UDC: 517.983.3+512.643.8+519.62
MSC: Primary 47B35; Secondary 15B05, 65F08, 65F15, 65L50
Language: English
Original paper language: Russian
Citation: A. Böttcher, C. Garoni, S. Serra-Capizzano, “Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey”, Mat. Sb., 208:11 (2017), 29–55; Sb. Math., 208:11 (2017), 1602–1627
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v208/i11/p29
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:481
    Russian version PDF:43
    English version PDF:15
    References:44
    First page:21
     
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