Optimal multilevel matrix algebra operators |
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Authors: | Fabio di Benedetto Stefano serra Capizzano |
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Affiliation: | a Dipartimento di Matematica, Genova, Italyb Dipartimento di Informatica, pisa, Italy |
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Abstract: | We study the optimal Frobenius operator in a general matrix vector space and in particular in the multilevel trigonometric matrix vector spaces, by emphasizing both the algebraic and geometric properties. These general results are used to extend the Korovkin matrix theory for the approximation of block Toeplitz matrices via trigonometric vector spaces. The abstract theory is then applied to the analysis of the approximation properties of several sine and cosine based vector spaces. Few numerical experiments are performed to give evidence of the theoretical results. |
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Keywords: | Masking operators Toeplitz matrices Matrix vector spaces and matrix algebras Korovkin theorem |
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