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By Vandebril R.

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Comparison in speed between the new and traditional approach 1000 Semi Separable svd Traditional svd 900 800 Number of iterations 700 600 500 400 300 200 100 0 50 100 150 200 250 300 Size of the matrices 350 400 450 500 Fig. 5. Number of implicit QR–steps Comparison in accuracy for singular values [0,1] −11 10 maximum relative error of the eigenvalues Semi Separable QR Traditional QR −12 10 −13 10 −14 10 −15 10 50 100 150 200 250 300 Size of the matrices 350 400 450 500 Fig. 6. Equal spaced singular values in (0, 1] the largest singular values, and the corresponding vectors, is needed [11,22, 23,28,29].

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Some applications of the rank revealing QR factorization. SIAM J. Sci. Stat. Comp. 13, 727–741 (1992) 4. : On rank-revealing factorizations. SIAM J. Matrix Anal. Appl. 15, 592–622 (1994) 194 Raf Vandebril et al. 5. : Accurate singular values of bidiagonal matrices. SIAM J. Sci. Comp. 11(5), 873–912 (1990) 6. : Some observations on inverses of band matrices and low rank perturbations of triangular matrices. Acta Technica Academiae Scientiarum Hungaricae. 108(1–2), 41–48 (1997–1999) 7. : Oscillation matrices and kernels and small vibrations of mechanical systems.

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A QR-method for computing the singular values via semiseparable matrices by Vandebril R.


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