The spectrum of a glued matrix

SIAM Journal on Matrix Analysis and Applications

Volumn 31, Issue 1, 2009, Pages 114-132

  Parlett, Beresford N ^a   Vömel, Christof ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Eigenvalue clusters; Glued matrix; Rank 1 gluing; Rank 2 gluing; Secular equation

Indexed keywords

EIGEN-VALUE; EIGENVALUE CLUSTERS; GLUED MATRIX; MATRIX RANK; SECULAR EQUATIONS;

EIGENVALUES AND EIGENFUNCTIONS; GLUING;

MATRIX ALGEBRA;

EID: 73649111069     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/070687062     Document Type: Conference Paper

References (19)

1. E. ANDERSON, Z. BAI, C. BISCHOF, S. BLACKFORD, J. DEMMEL, J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, AND D. SORENSEN, LAPACK User's Guide, 3rd ed., SIAM, Philadelphia, 1999.
2. R. M. BEAM AND R. F. WARMING, The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices, SIAM J. Sci. Comput., 14 (1993), pp. 971-1006.
3. J. BUNCH, P. NIELSEN, AND D. SORENSEN, Rank-one modification of the symmetric eigenproblem, Numer. Math., 31 (1978), pp. 31-48.
4. B. CAHLON, D. M. KULKARNI, AND P. SHI, Stepwise stability for the heat equation with a nonlocal constraint, SIAM J. Numer. Anal., 32 (1995), pp. 571-593.
5. J. J. M. CUPPEN, A divide and conquer method for the symmetric tridiagonal eigenproblem, Numer. Math., 36 (1981), pp. 177-195.
6. C. M. DA FONSECA, On the location of the eigenvalues of Jacobi matrices, Appl. Math. Lett., 19 (2006), pp. 1168-1174.
7. C. M. DA FONSECA, On the eigenvalues of some tridiagonal matrices, J. Comput. Appl. Math., 200 (2007), pp. 283-286.
8. J. W. DEMMEL, Applied Numerical Linear Algebra, SIAM, Philadelphia, 1997.
9. J. W. DEMMEL, O. A. MARQUES, B. N. PARLETT, AND C. VÖMEL, A Testing Infrastructure for Symmetric Tridiagonal Eigensolvers, Technical report LBNL-61831, Lawrence Berkeley National Laboratory, Berkeley, CA, 2006.
10. I. S. DHILLON, B. N. PARLETT, AND C. VÖMEL, Glued matrices and the MRRR algorithm, SIAM J. Sci. Comput., 27 (2005), pp. 496-510.
11. W. B. GRAGG AND W. J. HARROD, The numerically stable reconstruction of Jacobi spectral data, Numer. Math., 44 (1984), pp. 317-336.
12. R. GREGORY AND D. KARNEY, A Collection of Matrices for Testing Computational Algorithms, John Wiley, New York, 1969.
13. M. GU AND S. C. EISENSTAT, A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 172-191.
14. M. HEGLAND AND J. T. MARTI, Algorithms for the reconstruction of special Jacobi matrices from their eigenvalues, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 219-228.
15. D. KULKARNI, D. SCHMIDT, AND S.-K. TSUI, Eigenvalues of tridiagonal pseudo-Toeplitz matrices, Linear Algebra Appl., 297 (1999), pp. 63-80.
16. B. N. PARLETT, The Symmetric Eigenvalue Problem, SIAM, Philadelphia, 1998.
17. B. N. PARLETT AND C. VÖMEL, The Spectrum of a Glued Matrix, Technical report 579, Computer Science Department, ETH Zurich, Zurich, Switzerland, 2007.
18. J. H. WILKINSON, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford, UK, 1965.
19. S.-F. XU, On the Jacobi matrix inverse eigenvalue problem with mixed given data, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 632-639.