منابع مشابه
Generalized Golub-Kahan Bidiagonalization and Stopping Criteria
The Golub–Kahan bidiagonalization algorithm has been widely used in solving leastsquares problems and in the computation of the SVD of rectangular matrices. Here we propose an algorithm based on the Golub–Kahan process for the solution of augmented systems that minimizes the norm of the error and, in particular, we propose a novel estimator of the error similar to the one proposed by Hestenes a...
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Classical matrix perturbation results, such as Weyl’s theorem for eigenvalues andthe Davis-Kahan theorem for eigenvectors, are general purpose. These classicalbounds are tight in the worst case, but in many settings sub-optimal in the typicalcase. In this paper, we present perturbation bounds which consider the nature ofthe perturbation and its interaction with the unperturbed s...
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Generalized Cross Validation (GCV) is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small-scale problems, but prohibitively expensive to compute for large-scale ones. This paper describes a novel method, based on Gauss-type quadrature, for determining up...
متن کاملA useful variant of the Davis–Kahan theorem for statisticians
The Davis–Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. 10 It relies on an eigenvalue separation condition between certain relevant population and sample eigenvalues. We present a variant of this result that depends only on a population eigenvalue separation condition, ma...
متن کاملReorthogonalization for the Golub-Kahan-Lanczos bidiagonal reduction
The Golub–Kahan–Lanczos (GKL) bidiagonal reduction generates, by recurrence, the matrix factorization of X ∈ Rm×n,m ≥ n, given by X = U BV T where U ∈ Rm×n is left orthogonal, V ∈ Rn×n is orthogonal, and B ∈ Rn×n is bidiagonal. When the GKL recurrence is implemented in finite precision arithmetic, the columns of U and V tend to lose orthogonality, making a reorthogonalization strategy necessary...
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ژورنال
عنوان ژورنال: Slavic Review
سال: 1982
ISSN: 0037-6779,2325-7784
DOI: 10.1017/s0037677900156992