Orthogonal rational functions and diagonal-plus-semiseparable matrices

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 4791, Issue , 2002, Pages 162-170

  Van Barel, Marc ^a   Fasino, Dario ^b   Gemignani, Luca ^c   Mastronardi, Nicola ^d  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF UDINE   (Italy)

^c UNIVERSITY OF PISA   (Italy)

^d CNR   (Italy)

Author keywords

Diagonal plus semiseparable matrices; Inverse eigenvalue problems; Orthogonal rational functions; Recurrence relation

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; INTERPOLATION; INVERSE PROBLEMS; MATRIX ALGEBRA; POLES AND ZEROS;

INVERSE EIGENVALUE PROBLEMS; ORTHOGONAL RATIONAL FUNCTIONS; RECURRENCE RELATION;

SIGNAL PROCESSING;

EID: 0036992465     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.453815     Document Type: Conference Paper

References (18)

1. A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad, Orthogonal rational functions, vol. 5 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 1999.
2. A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad, "Orthogonal rational functions with poles on the unit circle," J. Math. Anal. Appl. 182(1), pp. 221-243, 1994.
3. M. Van Barel and A. Bultheel, "Discrete linearized least-squares rational approximation on the unit circle," J. Comput. Appl. Math. 50(1-3), pp. 545-563, 1994.
4. V. Olshevsky and V. Y. Pan, "Polynomial and rational evaluation and interpolation (with structured matrices)," Automata, languages and programming (Prague 1999), 585-594, Lecture Notes in Comput. Sci., 1644, Springer, Berlin, 1999.
5. Ph. Delsarte, Y. Genin and Y. Kamp, "On the role of the Nevanlinna-Pick problem in circuit and system theory," Internat. J. Circuit Theory Appl. 9 (1981), 177-187.
6. W.B. Gragg and A. Lindquist, "On the partial realization problem," Linear Algebra Appl. 50 (1983), 277-319.
7. A. Bultheel and M. Van Barel, "Padé techniques for model reduction in linear system theory," J. Comput. Appl. Math. 14 (1986), 401-438.
8. A. Bultheel and B. De Moor, "Rational approximation in linear systems and control," J. Comput. Appl. Math. 121 (2000), 355-378.
9. B. Ninness and F. Gustafsson, "A unifying construction of orthonormal bases for system identification," IEEE Trans. Automat. Control 42 (1997), 515-521.
10. W. Gautschi, "The use of rational functions in numerical quadrature," J. Comput. Appl. Math. 133 (2001), 111-126.
11. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, "Quadrature and orthogonal rational functions," J. Comput. Appl. Math. 127 (2001), 67-91.
12. L. Reichel, "Construction of polynomials that are orthogonal with respect to a discrete bilinear form," Adv. Comput. Math. 1 (1993), 241-258.
13. L. Reichel, "Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation," SIAM J. Matrix Anal. Appl. 12 (1991), 552-564.
14. D. Fasino and L. Gemignani, "A Lanczos-type algorithm for the QR factorization of regular Cauchy matrices," Numer. Lin. Algebra with Appl., 2000. To appear.
15. W. B. Gragg and W. J. Harrod, "The numerically stable reconstruction of Jacobi matrices from spectral data," Numer. Math. 44, pp. 317-335, 1984.
16. F. R. Gantmacher and M. G. Kreǐn, Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme, Akademie-Verlag, Berlin, 1960.
17. D. Fasino and L. Gemignani, "Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices," 2001, submitted.
18. D. Fasino and L. Gemignani, "A Lanczos-type algorithm for the QR factorization of regular Cauchy matrices," Numer. Linear Algebra Appl. 9 (2002), 305-319.