Geodesic
Exploration of Toeplitz-like matrices with unbounded symbols is not a~purely academic journey
Sbornik. Mathematics, Tome 208 (2017) no. 11, pp. 1602-1627

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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. 
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     title = {Exploration of {Toeplitz-like} matrices with unbounded symbols is not a~purely academic journey},
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A. Böttcher; C. Garoni; S. Serra-Capizzano. Exploration of Toeplitz-like matrices with unbounded symbols is not a~purely academic journey. Sbornik. Mathematics, Tome 208 (2017) no. 11, pp. 1602-1627. http://geodesic.mathdoc.fr/item/SM_2017_208_11_a2/