Four short stories about Toeplitz matrix calculations

By Thomas Strohmer. 2000

60 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/05e43335463a1a76c82b42247b2988f1f3fb01db

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Wiener's lemma for infinite matrices with polynomial off-diagonal decay (2005, background): “The classical Wiener’s lemma and its various generalizations (see, for instance, [3,8,9,12–14]) are impo have numerous applications, for instance, in numerical analysis [4,17,18], wavelets and affine frames [5,1”
Wiener’s Lemma for Infinite Matrices II (2007, methodology): “... classical Wiener’s lemma and its weighted variation ([25]) were used to establish the decay property at infinity for dual generators of a shift-invariant space ([1, 27]); the Wiener’s lemma for matrices associated with twisted convolution was used in the study the decay properties of the dual Ga”
Convergence Analysis of the Finite Section Method and Banach Algebras of Matrices (2010, background): “[17, 25, 26, 28] the matrix entries do decay off the diagonal, but thresholding would still leave us with banded matrices with the number of non-zero diagonals easily in the order of several dozens.”
Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices (2006, methodology): “We mention Jaffard’s “lemme de fenetre and perturbation the ory [24], the finite section method for operator equations [21, 35] and for frames [9], local error estimates of wavelet and Gabor expansions [1], or the time-frequency decay of dual Gabor windows [17].”
Stability of Localized Operators (2008, methodology): “For example, the classical Wiener’s lemma and its weighted variation ([39]) were used to establish the decay property at infinity for dual generators of a shift-invariant space ([1,43]); the Wiener’s lemma for matrices associated with twisted convolution was used in the study the decay properties of”