Naslov
Implementation of Jacobi rotations for accurate singular value computation in floating-point arithmetic

Autori
Drmač, Zlatko

Izvornik
SIAM journal on scientific computing (1064-8275) 18 (1997), 4; 1200-1222

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

Ključne riječi
Jacobi method ; modified Jacobi rotation ; relative accuracy ; singular values

Sažetak
In this paper we consider how to compute the singular value decomposition (SVD) $A=U\Sigma^T$ of $A=[a_1, a_2]\in R^{;m\times 2};$ accurately in floating point arithmetic. It is shown how to compute the Jacobi rotation $V$ (the right singular vector matrix) and how to compute $AV=U\Sigma$ even if the floating point epresentation of V is the identity matrix. In the case $\|a_1\|_2\gg \|a_2\|_2$, underflow can produce the identity matrix as the floating point value of V, even for $a_1$, $a_2$ that are far from being mutually orthogonal. This can cause loss of accuracy and failure of onvergence of the floating point implementation of the Jacobi method for computing the SVD. The modified Jacobi method recommended in this paper can be implemented as a reliable and highly accurate procedure for computing the SVD of general real matrices whenever the exact singular values do not exceed the underflow and overflow limits.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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