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• W2020954443 abstract "For a given nonnegative integer g, a matrix $A_n$ of size n is called g-Toeplitz if its entries obey the rule $A_n=[a_{r-gs}]_{r,s=0}^{n-1}$. Analogously, a matrix $A_n$ again of size n is called g-circulant if $A_n=bigl[a_{(r-g s) mathrm{mod},n}bigr]_{r,s=0}^{n-1}$. Such matrices arise in wavelet analysis, subdivision algorithms, and more generally when dealing with multigrid/multilevel methods for structured matrices and approximations of boundary value problems. In this paper we study the singular values of g-circulants and provide an asymptotic analysis of the distribution results for the singular values of g-Toeplitz sequences in the case where ${a_k}$ can be interpreted as the sequence of Fourier coefficients of an integrable function f over the domain $(-pi,pi)$. Generalizations to the block and multilevel case are also considered." @default.
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• W2020954443 date "2010-01-01" @default.
• W2020954443 modified "2023-10-17" @default.
• W2020954443 title "Spectral Features and Asymptotic Properties for <i>g</i>-Circulants and <i>g</i>-Toeplitz Sequences" @default.
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• W2020954443 doi "https://doi.org/10.1137/090760209" @default.
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