engleski

New fast and accurate Jacobi SVD algorithm. II

This paper presents new one--sided Jacobi SVD algorithm for triangular matrices. New pivot strategy exploits the triangular form and additional structure if the input triangular matrix is the result of rank revealing QR factorization. If used in the preconditioned Jacobi SVD algorithm, described in the first part of this report, it delivers superior performance leading to the currently fastest method for computing SVD decomposition with high relative accuracy. Furthermore, the efficiency of the new algorithm is comparable to the less accurate bidiagonalization based methods. The paper also discusses underflow issues in floating point implementation, and shows how to use perturbation theory to fix the imperfectness of machine arithmetic.

Jacobi method; singular value decomposition; eigenvalues

Ovaj rad je (zajedno s radom 336321) nagradjen prestižnom strukovnom nagradom SIAG/Linear Algebra Prize, za najbolji rad u području primijenjene linearne algebre u trogodišnjem periodu, http://www.siam.org/prizes/sponsored/siagla.php O nagradjenim radovima se može pročitati u SIAM News na URL adresi http://www.siam.org/pdf/news/1696.pdf