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- W3148217076 abstract "and Applied Analysis 3 The first and second terms S 1 and S 2 are called sample error which will be studied in Section 5, while the third termD(λ) is regularization error (or approximation error) which is our main work in this paper. It is known that f λ can be freely chosen in H K which is close to f ρ in some sense and in previous work f λ is always naturally chosen to be the oneminimizingD(λ). However, we will encounter difficulties if the minimizer does not exist or the expression of the minimizer is not explicit. In this paper, we construct a special function in the form f λ = (L α K + λ β I) −1 L α K f ρ (15) with some α, β > 0 to handle this problem. 4. Regularization Error It is the main contribution of this section to conduct error analysis for the regularization error. Regularization error, also called approximation error, has already been studied in [18]. However, we will analyze this part of error in a different viewpoint. From [1], we know L K is a compact self-adjoint and positive operator. By applying the spectral theorem for compact operators, we can bound a compact positive operator with its eigenvalues. Firstly, we have to introduce a useful lemma. Lemma 5. Let a, b, c, d > 0 and c < d; one has" @default.
- W3148217076 created "2021-04-13" @default.
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- W3148217076 date "2015-01-01" @default.
- W3148217076 modified "2023-09-27" @default.
- W3148217076 title "Constructive Analysis for Least Squares Regression with Generalized K-Norm Regularization" @default.
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