Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation

Linear Algebra and Its Applications

Volumn 324, Issue 1-3, 2001, Pages 133-146

  Oishi, Shin'ichi ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

Bauer Fike type theorem; Rounding mode controlled computation; Verified eigenvalue computation; Weyl type theorem

Indexed keywords

EID: 0035630729     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(00)00272-X     Document Type: Article

References (6)

1. S. Oishi, S.M. Rump, Fast verification of solutions of matrix equations, Numer. Math., submitted.
2. Bauer F., Fike C. Norms and exclusion theorems. Numer. Math. 2:1960;137-141.
3. G.W. Stewart, J. Sun, Matrix Perturbation Theory, Academic Press, New York, 1990, p. 203.
4. G. Golub, C. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1983.
5. Eisenstat S.C., Ipsen I.C.F. Relative perturbation techniques for singular value problems. SIAM J. Numer. Anal. 32(6):1995;1972-1988.
6. Golub G., Kahan W. Calculating the singular values and pseudo-inverse of matrix. SIAM J. Numer. Anal. Ser. B. 2:1965;205-224.