journal article May 01, 1987

On condition numbers and the distance to the nearest ill-posed problem

View at Publisher Save 10.1007/bf01400115
Topics

No keywords indexed for this article. Browse by subject →

References
19
[1]
Demmel, J.: The condition number of equivalence transformations which block diagonalize matrix pencils. SIAM J. Numer. Anal.20, 599?601 (1983) 10.1137/0720040
[2]
Demmel, J.: Computing stable eigendecompositions of matrices. Linear Algebra Appl.79:163?193 (1986) 10.1016/0024-3795(86)90298-3
[3]
Demmel, J.: On the conditioning of pole assignment. Computer Science Dept. Report # 150. Courant Institute of Mathematical Sciences. New York, Jan. 1985
[4]
Eckart, C., Young, G.: A principal axis transformation for non-hermitian matrices. Bull. Am. Math. Soc., New Ser45, 118?121 (1939) 10.1090/s0002-9904-1939-06910-3
[5]
Golub, G., Van Loan C: Matric computations. Baltimore: Johns Hopkins Press 1983
[6]
Hartman, P.: Ordinary differential equations. New York: John Wiley 1973
[7]
Hough, D.: Explaining and ameliorating the ill condition of zeros of polynomials. Thesis. Mathematics Department, University of California, Berkeley, CA 1977 10.21236/ada040476
[8]
Kahan, W.: Numerical linear algebra. Can. Math. Bull.9, 757?801 (1966) 10.4153/cmb-1966-083-2
[9]
Kahan, W.: Conserving confluence curbs ill-condition. Computer Science Dept. Report. University of California. Berkeley 1972
[10]
Kato, T.: Perturbation theory for linear operators. Berlin. Heidelberg, New York: Springer 1966.
[11]
Kautsky, J., Nichols, N., Van Dooren, P.: Robust pole assignment in linear state feedback. Int. J Control41, 1129?1155 (1985) 10.1080/0020718508961188
[12]
Parlett, B. N., Ng, K. C.: Development of an accurate algorithm for exp(B?). Report PAM-294. Center for Pure and Applied Mathematics. University of California. Berkeley. August 1985
[13]
Ruhe, A.: Properties of a matrix with a very ill-conditioned eigenproblem. Numer. Math.15, 57?60 (1970) 10.1007/bf02165660
[14]
Stewart, G.W.: Error bounds for approximate invariant subspaces of closed linear operators SIAM J. Numer. Anal.8 796?808 (1971) 10.1137/0708073
[15]
Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford Clarendon Press 1965
[16]
Wilkinson, J.H.: Note on matrices with a very ill-conditioned eigenproblem. Numer. Math.19, 176?178 (1972) 10.1007/bf01402528
[17]
Wilkinson, J.H.: On neighboring matrices with quadratic elementary divisors. Numer. Math.44, 1?21 (1984) 10.1007/bf01389751
[18]
Wilkinson, J.H.: Sensitivity of eigenvalues. Util. Math.25, 5?76.
[19]
Wonham, W.M.: Linear multivariable control.: A geometric approach. 2nd edition. Berlin- Heidelberg, New York: Springer 1979 10.1007/978-1-4684-0068-7
Cited By
221
IEEE Transactions on Geoscience and...
Linear Algebra and its Applications
Metrics
221
Citations
19
References
Details
Published
May 01, 1987
Vol/Issue
51(3)
Pages
251-289
License
View
Cite This Article
James Weldon Demmel (1987). On condition numbers and the distance to the nearest ill-posed problem. Numerische Mathematik, 51(3), 251-289. https://doi.org/10.1007/bf01400115
Related

You May Also Like

A note on two problems in connexion with graphs

E. W. Dijkstra · 1959

23,563 citations

Image recovery via total variation minimization and related problems

Antonin Chambolle, Pierre-Louis Lions · 1997

1,190 citations