New rigorous perturbation bounds for the Cholesky-like factorization of skew-symmetric matrix
نویسندگان
چکیده
منابع مشابه
Rigorous Multiplicative Perturbation Bounds for the Generalized Cholesky Factorization and the Cholesky–like Factorization
The generalized Cholesky factorization and the Cholesky-like factorization are two generalizations of the classic Cholesky factorization. In this paper, the rigorous multiplicative perturbation bounds for the two factorizations are derived using the matrix equation and the refined matrix equation approaches. The corresponding first-order multiplicative perturbation bounds, as special cases, are...
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As will be shown in this paper, there always exists an R such that (1.1) holds. We present a stable O(n3) algorithm that computes an R that has the form of a permuted triangular matrix. Our motivation comes from eigenvalue problems with Hamiltonian structure. A matrix H ∈ R is said to be Hamiltonian if (JH) = JH and skew-Hamiltonian if (JH) = −JH . EXAMPLE 1. The study of corner singularities i...
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This article presents rigorous normwise perturbation bounds for the Cholesky, LU and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. The used approach is a combination of the classic and refined matrix equation approaches. Each of th...
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Let K be a symmetric indefinite matrix. Suppose that K 1⁄4 LJL is the generalized Cholesky factorization of K. In this paper we present perturbation analysis for the generalized Cholesky factorization. We obtain the first-order bound on the norm of the perturbation in the generalized Cholesky factor. Also, we give rigorous perturbation bounds. 2002 Elsevier Inc. All rights reserved.
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Sparse linear equations Kd r are considered, where K is a specially structured symmetric indefinite matrix that arises in numerical optimization and elsewhere. Under certain conditions, K is quasidefinite. The Cholesky factorization PKP T LDL T is then known to exist for any permutation P, even though D is indefinite. Quasidefinite matrices have been used successfully by Vanderbei within barrie...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.02.032