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.

Optimal multilevel matrix algebra operators

DI BENEDETTO, FABIO;
2000-01-01

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/188548
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