Have a personal or library account? Click to login
Why Perturbations? Cover

References

  1. 1. Bernstein, D. S. Matrix Mathematics: Theory, Facts and Formulas. Princeton, NJ, Prinston, 2009. ISBN 978-0-691-13287-7.10.1515/9781400833344
  2. 2. Bhatia, R. Matrix Factorizations and Their Perturbations. – Linear Algebra App., Vol. 197-198, 1994, pp. 245-276. DOI: 10.1016/0024-3795(94)90490-1.10.1016/0024-3795(94)90490-1
  3. 3. Bhatia, R. Matrix Analysis. New York, Springer, 1997. ISBN 978-1-4612-6857-4.
  4. 4. Chen, X. S., W. Li, M. K. Ng. Perturbation Analysis for Antitriangular Schur Decomposition. – SIAM J. Matrix Analysis App., Vol. 33, 2012, pp. 1328-1340. DOI: 10.1137/110841370.10.1137/110841370
  5. 5. Demmel, J. W. On Condition Numbers and the Distance to the Nearest Ill-Posed Problem. – Numer. Math., Vol. 51, 1987. DOI: 10.1007/BF01400115.10.1007/BF01400115
  6. 6. Gantmacher, F. R. Theory of Matrices. Vol. 1, 2. New York, Chelsea, 1959. Reprinted by the AMS, 2000. ISBN 0-8218-2664-6.
  7. 7. Kato, T. Perturbation Theory for Linear Operators. 2nd Ed. Berlin, Springer-Verlag, 1995. ISBN 978-0-540-58661-6.
  8. 8. Konstantinov, M., D. W. Gu, V. Mehrmann, P. Petkov. Perturbation Theory for Matrix Equations. North-Holland, Amsterdam, Elsevier, 2003. XII+429 p. ISBN 978-0444-51315-9.
  9. 9. Konstantinov, M., P. Petkov. The Method of Splitting Operators and Lyapunov Majorants in Perturbation Linear Algebra and Control. – Numerical Functional Analysis and Optimization, Vol. 23, 2002, pp. 529-572. DOI: 10.1081/NFA-120014751.10.1081/NFA-120014751
  10. 10. Konstantinov, M., P. Petkov. Sensitivity Analysis of Unitary Matrix Decompositions. – Tensor, N. S., Vol. 64, 2003, pp. 72-92. ISSN 0040-3504.
  11. 11. Konstantinov, M. M., P. H. Petkov. Perturbation Methods in Linear Algebra and Control (Survey). – Applied and Computational Mathematics, Vol. 7, 2008, pp. 141-161. ISSN 1683-3511.
  12. 12. Konstantinov, M. M., P. H. Petkov. Perturbation Analysis of Matrix Equations and Decompositions. – In: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Festschrift in Honor of Volker Mehrmann. P. Benner, M. Bollhöfer, D. Kressner, C. Mehl, T. Stykel, Eds. Heidelberg, Springer, 2015, pp. 161-197. ISBN: 978-3-319-15259-2. DOI: 10.1007/978-3-319-15260-8.10.1007/978-3-319-15260-8
  13. 13. Konstantinov, M. M., P. H. Petkov, N. D. Christov. Nonlocal Perturbation Analysis of the Schur System of a Matrix. – SIAM J. Matrix Analysis App., Vol. 15, 1994, pp. 383-392. DOI: 10.1137/S089547989120267X.10.1137/S089547989120267X
  14. 14. Lancaster, P., M. Tismenetsky. The Theory of Matrices. 2nd Ed. Academic. Orlando, FL, 1985.
  15. 15. Petkov, P. H., N. D. Christov, M. M. Konstantinov. A New Approach to the Perturbation Analysis of Linear Control Problems. – In: Preprints of the 11th IFAC Congress, Tallin, Estonia, 1990, pp. 311-316.
  16. 16. Schrödinger, E. Collected Papers on Wave Mechanics. London, Blackie & Son Limited, 1928.
  17. 17. Strutt, J. W., Lord Rayleigh. The Theory of Sound. 2nd Ed. 1894. New York, Dover Publications, 1945.
  18. 18. Stewart, G. W. Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators. – SIAM J. Numer. Anal., Vol. 8, 1971, pp. 796-808. DOI: 10.1137/0708073.10.1137/0708073
  19. 19. Stewart, G. W. Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems. – SIAM Review, Vol. 15, 1973, pp. 727-764. DOI: 10.1137/1015095.10.1137/1015095
  20. 20. Stewart, G. W., J.-G. Sun. Matrix Perturbation Theory. New York, Academic Press, 1990. ISBN 978-0126702309.
  21. 21. Sun, J.-G. Perturbation Bounds for the Generalized Schur Decomposition. – SIAM J. Matrix Analysis App., Vol. 16, 1995, pp. 1328-1340. DOI: 10.1137/S0895479892242189.10.1137/S0895479892242189
DOI: https://doi.org/10.2478/cait-2020-0054 | Journal eISSN: 1314-4081 | Journal ISSN: 1311-9702
Language: English
Page range: 170 - 175
Published on: Dec 10, 2020
Published by: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2020 Ivan Popchev, published by Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.