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.
Fat diagonals and Fourier analysis
SERRA CAPIZZANO, STEFANO
2003-01-01
Abstract
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.
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