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Behavior of a functional in learning theory |
| SUN Hongwei |
| School of Science, Jinan University, Jinan 250022, China; School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
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Abstract Let H be a Hilbert space, A ∈ L(H), y ∈ R(A), and y ∈R(A). We study the behavior of the distance square between y and A(Bτ), defined as a functional F(τ), as the radius τ of the ball Bτ of H tends to ∞. This problem is important in estimating the approximation error in learning theory. Our main result is to estimate the asymptotic behavior of F(τ) without the compactness assumption on the operator A. We also consider the Peetre K-functional and its convergence rates.
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Issue Date: 05 September 2007
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