Rounding error and perturbation bounds for the symplectic QR factorization

To compute the eigenvalues of a skew-symmetric matrix A, we can use a one-sided Jacobi-like algorithm to enhance accuracy. This algorithm begins by a suitable Cholesky-like factorization of A, A=G T JG . In some applications, A is given implicitly in that form and its natural Cholesky-like factor G...

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Vydané v:Linear algebra and its applications Ročník 358; číslo 1; s. 255 - 279
Hlavní autori: Singer, Sanja, Singer, Saša
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 2003
Predmet:
Perturbation bounds
Rounding error bounds
Skew-symmetric eigenproblem
Symplectic QR factorization
Skew-symmetric eigenproblem
Symplectic QR factorization
Rounding error bounds
Perturbation bounds
ISSN:0024-3795, 1873-1856
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Popis
Shrnutí:To compute the eigenvalues of a skew-symmetric matrix A, we can use a one-sided Jacobi-like algorithm to enhance accuracy. This algorithm begins by a suitable Cholesky-like factorization of A, A=G T JG . In some applications, A is given implicitly in that form and its natural Cholesky-like factor G is immediately available, but “tall”, i.e., not of full row rank. This factor G is unsuitable for the Jacobi-like process. To avoid explicit computation of A, and possible loss of accuracy, the factor has to be preprocessed by a QR-like factorization. In this paper we present the symplectic QR algorithm to achieve such a factorization, together with the corresponding rounding error and perturbation bounds. These bounds fit well into the relative perturbation theory for skew-symmetric matrices given in factorized form.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(02)00263-X