Generalization of the Bauer-Fike theorem. (English) Zbl 0579.15006
The Bauer-Fike theorem for diagonalizable matrices is generalized to cases where (i) non-diagonalizable matrices or (ii) only part of the spectrum, is considered.
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 93B55 | Pole and zero placement problems |
References:
| [1] | Bauer, F.L., Fike, E.T.: Norms and Exclusion Theorems. Numer. Math.2, 137-144 (1960) · Zbl 0101.25503 · doi:10.1007/BF01386217 |
| [2] | Bauer, F.L., Householder, A.S.: Absolute Norms and Characteristic Roots. Numer. Math.3, 241-246 (1961) · Zbl 0111.01601 · doi:10.1007/BF01386023 |
| [3] | Chu, K.E., Nichols, N.K.: Robust Pole Assignment by Output Feedback. Proc. 4th Intern. Conf. on Control Theory, Cambridge, U.K., September 1984 · Zbl 0584.93026 |
| [4] | Chu, K.E.: Exclusion Theorems and The Perturbation Analysis of The Generalized Eigenvalue Problem. Dept. of Maths., Univ. of Reading, U.K., Num. Anal. Rpt. NA/11/85, 1985 |
| [5] | Golub, G.H., Van Loan, C.: Matrix Computations. The Johns Hopkins University Press, Baltimore 1983 |
| [6] | Golub, G.H., Wilkinson, J.H.: Ill-Conditioned Eigensystems and The Computation of The Jordan Canonical Form. SIAM Rev.18, 578-619 (1976) · Zbl 0341.65027 · doi:10.1137/1018113 |
| [7] | Householder, A.S.: The Theory of Matrices in Numerical Analysis. New York: Dover Publications 1974 · Zbl 0255.65027 |
| [8] | Kautsky, J., Nichols, N.K.: Robust Eigenstructure Assignment in State Feedback Control. Dept. of Maths., Univ. of Reading, Num. Anal. Rpt. NA 2/83, 1983 · Zbl 0521.93020 |
| [9] | Klein, G.: On the Relationship between Controllability Indexes, Eigenvector Assignment and Deadbeat Control. IEEE Trans. Autom. Control. AC29, 77-79 (1984) · Zbl 0541.93026 · doi:10.1109/TAC.1984.1103380 |
| [10] | Stewart, G.W.: Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems. SIAM Rev.15, 727-764 (1973) · Zbl 0297.65030 · doi:10.1137/1015095 |
| [11] | Van Dooren, P.: Deadbeat Control: A Special Inverse Eignevalue Problem. BIT24, 681-699 (1984) · Zbl 0549.93019 · doi:10.1007/BF01934924 |
| [12] | Wilkinson, J.H.: The Algebraic Eigenvalue Problem. London: Oxford University Press 1965 · Zbl 0258.65037 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
