Computing the Singular Value Decomposition with High Relative Accuracy

@inproceedings{Demmel1997ComputingTS,
  title={Computing the Singular Value Decomposition with High Relative Accuracy},
  author={James Demmel and Ming Gu and Stanley C. Eisenstat and Ivan Slapnicar and Kresimir Veselic and Zlatko Drmac},
  year={1997}
}
We analyze when it is possible to compute the singular values and singular vectors of a matrix with high relative accuracy. This means that each computed singular value is guaranteed to have some correct digits, even if the singular values have widely varying magnitudes. This is in contrast to the absolute accuracy provided by conventional backward stable algorithms, which in general only guarantee correct digits in the singular values with large enough magniturds. It is of interest to compute… CONTINUE READING
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References

Publications referenced by this paper.
SHOWING 1-10 OF 55 REFERENCES

Jacobi's Method is More Accurate than QR

  • SIAM J. Matrix Analysis Applications
  • 1989
VIEW 35 EXCERPTS
HIGHLY INFLUENTIAL

LAPACK Users' Guide (second edition)

E. Anderson, Z. Bai, +8 authors D. Sorensen
  • SIAM, Philadelphia
  • 1995
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Total Positivity

S. Karlin
  • Stanford University Press
  • 1968
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Accurate Eigensystem Computations by Jacobi Methods

  • SIAM J. Matrix Analysis Applications
  • 1995
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL