Fat diagonals and Fourier analysis

Fat diagonals and Fourier analysis

We use Fourier analysis and Toeplitz matrices to study the effect on matrix norms obtained by various "truncations" of the matrix. Examples include the truncation of a matrix to a central band of diagonals, truncation to the off-diagonal part, and the upper-triangular truncation. Our tools...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2003, Vol.24 (4), p.1060-1070
Hauptverfasser: HLADNIK, Milan, HOLBROOK, John, SERRA CAPIZZANO, Stefano
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Applied mathematics
Eigenvalues
Exact sciences and technology
Fourier analysis
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematical functions
Mathematics
Norms
Operator theory
Sciences and techniques of general use
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Beschreibung
Zusammenfassung:We use Fourier analysis and Toeplitz matrices to study the effect on matrix norms obtained by various "truncations" of the matrix. Examples include the truncation of a matrix to a central band of diagonals, truncation to the off-diagonal part, and the upper-triangular truncation. Our tools include tensor product constructions, asymptotic eigenvalue distributions, and multilevel Toeplitz matrices.
ISSN:0895-4798
1095-7162
DOI:10.1137/S0895479802411742