Naslov
Rounding error and perturbation bound for the symplectic QR factorization

Autori
Singer, Sanja ; Singer, Saša

Izvornik
Linear Algebra and its Applications (0024-3795) 358 (2003); 255-279

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Symplectic QR factorization; Rounding error bounds; perturbation bounds

Sažetak
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 $A$, $A = G^{T} J G$. 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA