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• W1988678429 endingPage "1559" @default.
• W1988678429 startingPage "1533" @default.
• W1988678429 abstract "We consider sequences of $scdot k(n)times tcdot k(n)$ matrices ${A_n(f)}$ with a block structure spectrally distributed as an $L_1$ $p$-variate $stimes t$ matrix-valued function $f$, and, for any $n$, we suppose that $A_n(cdot )$ is a linear and positive operator. For every fixed $n$ we approximate the matrix $A_n(f)$ in a suitable linear space $mathcal {M}_n$ of $scdot k(n)times tcdot k(n)$ matrices by minimizing the Frobenius norm of $A_n(f)-X_n$ when $X_n$ ranges over $mathcal {M}_n$. The minimizer $hat {X}_n$ is denoted by $mathcal {P}_{k(n)}(A_n(f))$. We show that only a simple Korovkin test over a finite number of polynomial test functions has to be performed in order to prove the following general facts: the sequence ${mathcal {P}_{k(n)}(A_n(f))}$ is distributed as $f$, the sequence ${A_n(f)-mathcal {P}_{k(n)}(A_n(f))}$ is distributed as the constant function $0$ (i.e. is spectrally clustered at zero). The first result is an ergodic one which can be used for solving numerical approximation theory problems. The second has a natural interpretation in the theory of the preconditioning associated to cg-like algorithms." @default.
• W1988678429 created "2016-06-24" @default.
• W1988678429 creator A5053268193 @default.
• W1988678429 date "2000-03-06" @default.
• W1988678429 modified "2023-09-27" @default.
• W1988678429 title "Korovkin tests, approximation, and ergodic theory" @default.
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• W1988678429 doi "https://doi.org/10.1090/s0025-5718-00-01217-5" @default.
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