Pseudospectra of matrix polynomials that are expressed in alternative bases

Mathematics in Computer Science

Volumn 1, Issue 2, 2007, Pages 353-374

  Corless, Robert M ^a   Rezvani, Nargol ^b   Amiraslani, Amirhossein ^c  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b UNIVERSITY OF TORONTO   (Canada)

^c UNIVERSITY OF CALGARY   (Canada)

Author keywords

Conditioning; Lebesgue constants; Lebesgue functions; Matrix polynomial; Pseudospectra

Indexed keywords

EID: 36448993054     PISSN: 16618270     EISSN: 16618289     Source Type: Journal    
DOI: 10.1007/s11786-007-0010-x     Document Type: Conference Paper

References (21)

1. A. Amiraslani. Algorithms for Matrices, Polynomials, and Matrix Polynomials. PhD thesis, University of Western Ontario, London, Canada, May 2006.
2. A. Amiraslani, D. A. Aruliah, and R. M. Corless. The Rayleigh quotient iteration for generalized companion matrix pencils. Submitted, 2006.
3. A. Amiraslani, R. M. Corless, and P. Lancaster. Linearization of matrix polynomials expressed in polynomial bases. Submitted, 2007.
4. D. A. Aruliah, R. M. Corless, L. Gonzalez-Vega, and A. Shakoori. Geometric applications of the Bézout matrix in the Lagrange basis. In Proceedings of SNC 2007, Jan Verschelde and Stephen M. Watt (editors), pages 55-64, ACM press, 2007.
5. J.-P. Berrut and L. N. Trefethen. Barycentric Lagrange interpolation. SIAM Review, 46(3):501-517, 2004.
6. Qi Chen and I. Babuška. Approximate optimal points for polynomial interpolation of a real function in an interval and in a triangle. Computer Methods in Applied Mechanics and Engineering, 128:405-417, 1995.
7. R. M. Corless. On a generalized companion matrix pencil for matrix polynomials expressed in the Lagrange basis. In D. Wang and L. Zhi (eds.), Symbolic-Numeric Computation, pages 1-18. Birkhäuser, 2006.
8. R. M. Corless and S. M. Watt. Bernstein bases are optimal, but, sometimes, Lagrange bases are better. In Proceedings of SYNASC, Timisoara, pages 141-153. MIRTON Press, September 2004.
9. R. M. Corless, S. M. Watt, and L. Zhi. QR factoring to compute the GCD of univariate approximate polynomials. IEEE Transactions on Signal Processing, 2004.
10. P. J. Davis. Circulant Matrices. Chelsea, 1994.
11. I. G. Gohberg, P. Lancaster, and L. Rodman. Matrix polynomials. Academic Press, 1982.
12. N. J. Higham. Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, second edition, 2002.
13. N. J. Higham. The numerical stability of barycentric Lagrange interpolation. IMA Journal of Numerical Analysis, 24:547-556, 2004.
14. N. J. Higham, D. S. Mackey, N. Mackey, and F. Tisseur. Symmetric linearizations for matrix polynomials. SIAM J. Matrix Anal. Appl., 29(1):143-159, 2006.
15. N. J. Higham, D. S. Mackey, and F. Tisseur. The conditioning of linearizations of matrix polynomials. SIAM J. Matrix Anal. Appl., 28(4):1005-1028, 2006.
16. P. Lancaster and P. Psarrakos. On the pseudospectra of matrix polynomials. SIAM J. Matrix Anal. Appl., 27:115-129, 2005.
17. D. Manocha and J. W. Demmel. Algorithms for intersecting parametric and algebraic curves II; multiple intersections. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 57(2):81-100, 1995.
18. I. Niven. Maxima and Minima without Calculus, Dolciani Mathematical Expositions, vol. 6., Mathematical Association of America, 1981.
19. T. Rivlin. Chebyshev Polynomials: From Approximation Theory to Number Theory. Wiley, 1990.
20. F. Tisseur. Backward error and condition of polynomial eigevnalue problems. Linear Algebra and its Applications, 309:339-361, 2000.
21. F. Tisseur and N. J. Higham. Structured pseudospectra for polynomial eigenvalue problems, with applications. SIAM J. Matrix Anal. Appl., 23(1):187-208, 2001.