Lanczos tridiagonalization, Golub-Kahan bidiagonalization and coreproblem
نویسندگان
چکیده
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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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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The concept of the core problem in total least squares (TLS) problems was introduced in [C. C. Paige and Z. Strakoš, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861–875]. It is based on orthogonal transformations such that the resulting problem decomposes into two independent parts, with one of the parts having trivial (zero) right-hand side and maximal dimensions, and the other part with nonzero...
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The symmetric Lanczos method is commonly applied to reduce large-scale symmetric linear discrete ill-posed problems to small ones with a symmetric tridiagonal matrix. We investigate how quickly the nonnegative subdiagonal entries of this matrix decay to zero. Their fast decay to zero suggests that there is little benefit in expressing the solution of the discrete ill-posed problems in terms of ...
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ژورنال
عنوان ژورنال: PAMM
سال: 2006
ISSN: 1617-7061,1617-7061
DOI: 10.1002/pamm.200610339