| Автор | Grammont, Laurence |
| Дата выпуска | 1994 |
| dc.description | The sensivtiity of the solution of the matrix Sylvester equation AX-XB=C is considered in the context of the classical perturbation theory. Our purpose is to find the most influent parameters in the sensitivity of the solution under perturbations in the data, and to compare the theoretical error bounds with numerical evidence. |
| Формат | application.pdf |
| Издатель | Marcel Dekker, Inc. |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Тема | Sylvester equation |
| Тема | condition number |
| Тема | departure from normality. |
| Название | On the numerical analtsys of generated sylvester equations |
| Тип | research-article |
| DOI | 10.1080/01630569408816591 |
| Electronic ISSN | 1532-2467 |
| Print ISSN | 0163-0563 |
| Журнал | Numerical Functional Analysis and Optimization |
| Том | 15 |
| Первая страница | 729 |
| Последняя страница | 754 |
| Аффилиация | Grammont, Laurence; Équipe d' Analyse Numérique de Lyon |
| Выпуск | 7-8 |
| Библиографическая ссылка | Ahues, M. and Chatelin, F. 1989. Exercices de valeurs propres de matrice, Paris: Masson Editeurs. |
| Библиографическая ссылка | Ahues, M. and Grammont, L. 1994. On the numerical analysis of Generalized Sylvester equations : First Part. Submitted to this journal, |
| Библиографическая ссылка | Barnett, S. and Storey, C. 1968. Some applications of the Lyapynov matrix equation. J. Inst. Math. Appl., 4: 33–42. |
| Библиографическая ссылка | Bartels, R. H. and Stewart, G. W. 1972. A solution of the equation AX-XB=C. Commun ACM, 15: 820–826. |
| Библиографическая ссылка | Chatelin, F. 1983. Spectral Approximation of Linear Operators, New York: Academic Press. |
| Библиографическая ссылка | Chastelin, F. 1987. Valeurs propres de matrices, Paris: Masson Editeurs. |
| Библиографическая ссылка | Chatelin, V., Fraysse, V. and Braconnier, T. 1993. Qualitative computing elements of a theory for finite precision computation, Cerfacs, , Inria: In : Workshop on Reliability of Computations. |
| Библиографическая ссылка | Dunford, N. and Schwartz, J. T. 1958. Linear Operators, Vol. 1 and 11, New York: Wiley Interscience. |
| Библиографическая ссылка | Djaferis, T. E. and Mitter, T. E. 1982. Algebraic methods for the study of some linear matrix equations. Linear Algebra and its applications, 44: 125–142. |
| Библиографическая ссылка | Gantmacher, F. R. 1959. The Theory of Matrices, New York: Chelsea. |
| Библиографическая ссылка | Golub, G. H., Nash, S. and Van Loan, Ch. 1979. A Hessenberg-Schur method for the problem AX-XB=C. IEEE transactions on automatic control, AC-24(6) |
| Библиографическая ссылка | Golub, G. H. and Van Loan, Ch. 1989. Matrix Computations, The Johns Hopkins University Press. |
| Библиографическая ссылка | Hartwig, R. 1972. Resultants and the solution of AX-XB=C. Siam. J. Appl. Math., 23: 104–117. |
| Библиографическая ссылка | Hearon, J. Z. 1977. Nonsingular Solutions of TA-BT=C. Linear Algebra and its applications, 16: 57–63. |
| Библиографическая ссылка | Henrici, P. 1962. Bounds for iterates, inverses, spectral variation and field of values of nonnormal matrices. Numer. Math., 4: 24–40. |
| Библиографическая ссылка | Higham, N. J. 1992. “Perturbation theory and backward error for AX-XB=C”. In Numerical Analysis RR N<sup>∘</sup> 211, University of Manchester. |
| Библиографическая ссылка | Hoskins, W. D., Meek, D. S. and Walton, D. J. 1977. A rapidly convergente method for the solution of the matrix equation -XA+AY-F. J. of Comp. and Appl. Math., 3: 211–215. |
| Библиографическая ссылка | Hoskins, W. D., Meek, D. S and Walton, D. J. 1979. High-order iterative methods for the solution of the matrix equation XA+AY-F. Linear Algebra and its applications, 23: 121–139. |
| Библиографическая ссылка | Jameson, A. 1968. Solution of the equation AX-XB=C by inversion of an M x M or N x N matrix. Siam. J. Appl. Math., 16: 1020–1023. |
| Библиографическая ссылка | Rothschild, D. and Jameson, A. 1970. Comparison of four numerical algorithms for solving the Lyapunov matrix equation. Int. J. Control, 2: 181–198. |
| Библиографическая ссылка | Kato, T. 1967. Perturbation Theory for Linear Operators, Berlin: Springer Verlag. |
| Библиографическая ссылка | Lancaster, P. 1969. Theory of Matrices, New York: Academic Press. |
| Библиографическая ссылка | Lancaster, P. 1970. Explicit solutions of linear matrix equations. Siam Review, 4: 544–599. |
| Библиографическая ссылка | Luenberger, D. G. 1971. An introduction to observers. IEEE Trans, on Autom. Control., AC-16(6) |
| Библиографическая ссылка | Mac Duffee, C. C. 1946. The Theory of Matrices Chelsea, New York |
| Библиографическая ссылка | Mastroerio, C. and Montrone, M. 1981. Un metodo a convergenza quadratica per equazioni matriciali lineari, Vol. 18, 87–96. Calcolo. |
| Библиографическая ссылка | Ruhe, A. 1979. SOR methods for eigenvalue problems with large sparse matrices. Math. Comp., 127: 695–710. |
| Библиографическая ссылка | Souz, E. and Bhattacharyya, S. P. 1981. Controllability observability and the solution of AX-XB-C. Linear Algebra and its applications, 39: 167–188. |
| Библиографическая ссылка | Starke, G. and Niethammer, W. 1991. SOR for AX-XB=C.. Linear Algebra and its applications, 39: 154,156–355,375. |
| Библиографическая ссылка | Wachspress, E. L. 1966. Iterative solution of elliptic systems, Prentice Hall. |
| Библиографическая ссылка | Wachspress, E. L. and Lu, A. 1991. Solution of Lyapunov equations by alternating direction implicit iteration. Math, Appl., 9: 43–58. |
| Библиографическая ссылка | Wilkinson, J. H. 1965. The Algebraic Eingenvalue Problem, Oxford University Press. |
| Библиографическая ссылка | Wimmer, H. 1989. Linear matrix equations : the module theoretical approach. Linear Algebra and its applications, 120: 149–164. |
| Библиографическая ссылка | Wimmer, H. and Ziebur, A. D. 1972. Solving the matrix equation . Siam Review, 14: 318–323. |
| Библиографическая ссылка | Wonham, W. M. 1979. A geometric approach. Linear multivariate control, New York: Springer Verlag. |
