Naslov
On Accurate Quotient Singular Value Computation in Floating-Point Arithmetic

Autori
Drmač, Zlatko ; Jessup, Elizabeth

Izvornik
SIAM Journal on Matrix Analysis and Applications (0895-4798) 22 (2000), 3; 853-873

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

Ključne riječi
generalized singular value decomposition; generalized eigenvalue problem; Jacobi method; regularization; relative accuracy; singular value decomposition

Sažetak
This paper presents a new algorithm for floating-point computation of the quotient singular value decomposition of an arbitrary matrix pair $(A, B) \in \mathbf{;R};^{;m \times n}; \times \mathbf{;R};^{;p \times n};$. In the case of full column rank $A$, the new algorithm computes all finite quotient singular values with high relative accuracy if $\min\{;\kappa_2(AD), \ D\ \mbox{;diagonal};\};$ is moderate and if an accurate rank revealing LU factorization of $B$ is possible. Numerical experiments show that in such a case the new algorithm computes the quotient singular values of all pairs $(AD, D_1 B D_2)$ with nearly the same accuracy, where $D$, $D_1$, $D_2$ are arbitrary diagonal nonsingular matrices.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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