Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices

Numerical Algorithms

Volumn 34, Issue 2-4, 2003, Pages 313-324

  Fasino, Dario ^a   Gemignani, Luca ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

Band matrices; Eigenvalue problems; Semiseparable matrices

Indexed keywords

EID: 4043086344     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000005402.66868.af     Document Type: Article

References (24)

1. D. Bini and L. Gemignani, Iteration schemes for the divide-and-conquer eigenvalue solver, Numer. Math. 67(4) (1994) 403-425.
2. D. Boley and G.H. Golub, A survey of matrix inverse eigenvalue problems, Inverse Problems 3 (1987) 595-622.
3. C.F. Borges and W.B. Gragg, A parallel divide and conquer algorithm for the generalized real symmetric definite tridiagonal eigenproblem, in: Numerical Linear Algebra, Kent, OH, 1992 (De Gruyter, Berlin, 1993) pp. 11-29.
4. S. Chandrasekaran and M. Gu, Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices, Linear Algebra Appl. 313(1-3) (2000) 107-114.
5. C. de Boor and G.H. Golub, The numerically stable reconstruction of a Jacobi matrix from spectral data, Linear Algebra Appl. 21(3) (1978) 245-260.
6. Y. Eidelman and I. Gohberg, Fast inversion algorithms for diagonal plus semiseparable matrices, Integral Equations Operator Theory 27(2) (1997) 165-183.
7. 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.
8. D. Fasino and L. Gemignani, Structural and computational properties of possibly singular semiseparable matrices, Linear Algebra Appl. 340 (2002) 183-198.
9. P. Favati, P. Rózsa, R. Bevilacqua and F. Romani, On the inverse of block tridiagonal matrices with applications to the inverses of band matrices and block band matrices, Oper. Theory Adv. Appl. 40 (1989) 447-469.
10. K.V. Fernando and B.N. Parlett, Differential qd algorithms, in: Numerical Linear Algebra, Kent, OH, 1992 (De Gruyter, Berlin, 1993) pp. 75-100.
11. F.R. Gantmacher and M.G. Kre in, Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme (Akademie-Verlag, Berlin, 1960).
12. G.H. Golub and C.F. Van Loan, Matrix Computations (John Hopkins Univ. Press, Baltimore, MD, 1989).
13. R.A. Gonzales, J. Eisert, I. Koltracht, M. Neumann and G. Rawitscher, Integral equation method for the continuous spectrum radial Schrödinger equation, J. Comput. Phys. 134(1) (1997) 134-149.
14. W.B. Gragg and W.J. Harrod, The numerically stable reconstruction of Jacobi matrices from spectral data, Numer. Math. 44 (1984) 317-335.
15. T. Kailath and A.H. Sayed, eds., Fast Reliable Algorithms for Matrices with Structure (SIAM, Philadelphia, PA, 1999).
16. D.P. Laurie, Accurate recovery of recursion coefficients from Gaussian quadrature formulas, J. Comput. Appl. Math. 112(1/2) (1999) 165-180.
17. N. Mastronardi, S. Chandrasekaran and S. Van Huffel, Fast and stable reduction of diagonal plus semi-separable matrices to tridiagonal and bidiagonal form, BIT 41 (2001) 149-157.
18. N. Mastronardi, S. Chandrasekaran and S. Van Huffel, Fast and stable two-way algorithm for diagonal plus semi-separable systems of linear equations, Numer. Linear Algebra Appl. 8(1) (2001) 7-12.
19. R. Nabben, Decay rates of the inverse of nonsymmetric tridiagonal and band matrices, SIAM J. Matrix Anal. Appl. 20 (1999) 820-837.
20. L. Reichel, Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation, SIAM J. Matrix Anal. Appl. 12 (1991) 552-564.
21. P. Rózsa, On the inverses of band matrices, Integral Equations Operator Theory 10 (1987) 82-95.
22. H. Rutishauser, Lectures on Numerical Mathematics (Birkhäuser, Boston, MA, 1990).
23. M. Van Barel, D. Fasino, L. Gemignani and N. Mastronardi, Orthogonal rational functions and structured matrices, Technical Report TW350, Department of Computer Science, Katholieke Universiteit Leuven, Belgium (2002) submitted.
24. L. Wuytack, An algorithm for rational interpolation similar to the qd-algorithm, Numer. Math. 20 (1972/73) 418-424.