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

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By Vandebril R.

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Anal. 2, 205–224 (1965) 10. : Matrix Computations. The Johns Hopkins university Press, third edition, 1996 11. : Principal component analysis. Springer verlag, 1986 12. : Linear complexity algorithm for semiseparable matrices. Integral Equations and Operator Theory. 29(3), 313–319 (1997) 13. : Some algorithms for solving special tridiagonal block toeplitz linear systems. J. Comput. Appl. Math. 156, 179–200 (2003) 14. : Matrix Algorithms, Vol II Eigensystems. SIAM, 1999 15. : The QLP approximation to the singular value decomposition.

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]. Once the upper triangular semiseparable matrix has been transformed to unreducible form, its singular values can be computed reapplying A QR–method for computing the singular values via semiseparable matrices 193 Comparison in accuracy for singular values 1:n −13 10 maximum relative error of the eigenvalues Semi Separable QR Traditional QR −14 10 −15 10 −16 10 50 100 150 200 250 300 Size of the matrices 350 400 450 500 Fig.

Numer. Anal. 2, 205–224 (1965) 10. : Matrix Computations. The Johns Hopkins university Press, third edition, 1996 11. : Principal component analysis. Springer verlag, 1986 12. : Linear complexity algorithm for semiseparable matrices. Integral Equations and Operator Theory. 29(3), 313–319 (1997) 13. : Some algorithms for solving special tridiagonal block toeplitz linear systems. J. Comput. Appl. Math. 156, 179–200 (2003) 14. : Matrix Algorithms, Vol II Eigensystems. SIAM, 1999 15. : The QLP approximation to the singular value decomposition.

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