Generalized diagonal pivoting methods for tridiagonal systems without interchanges

IAENG International Journal of Applied Mathematics

Volumn 40, Issue 4, 2010, Pages 1-7

  Erway, Jennifer B ^a   Marcia, Roummel F ^b   Tyson, Joseph A ^a  

^a WAKE FOREST UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Diagonal pivoting; Gaussian elimination; Linear algebra; Tridiagonal systems

Indexed keywords

EID: 78649902840     PISSN: 19929978     EISSN: 19929986     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. J. R. BUNCH AND B. N. PARLETT, Direct methods for solving symmetric indefinite systems of linear equations, SIAM J. Numer. Anal., 8, pp. 639-655, 1971.
2. J. R. BUNCH AND L. KAUFMAN, Some stable methods for calculating inertia and solving symmetric linear systems, Math. Comp., 31, pp. 163-179, 1977.
3. C. ASHCRAFT, R. G. GRIMES, AND J. G. LEWIS, Accurate symmetric indefinite linear equation solvers, SIAM J. Matrix Anal. Appl., 20, pp. 513-561, 1999.
4. H. R. FANG AND D. P. O'LEARY, Stable factorizations of symmetric tridiagonal and triadic matrices, SIAM J. Matrix Anal. Appl., 28, pp. 576-595, 2006.
5. J. R. BUNCH, Partial pivoting strategies for symmetric matrices, SIAM J. Numer. Anal., 11, pp. 521-528, 1974.
6. J. R. BUNCH AND R. F. MARCIA, A pivoting strategy for symmetric tridiagonal matrices, Numer. Linear Algebra Appl., 12, pp. 911-922, 2005.
7. J. R. BUNCH AND R. F. MARCIA, A simplified pivoting strategy for symmetric tridiagonal matrices, Numer. Linear Algebra Appl., 13, pp. 865-867, 2006.
8. J. B. ERWAY AND R. F. MARCIA, A backward stability analysis of diagonal pivoting methods for solving unsymmetric tridiagonal systems without interchanges. Numerical Linear Algebra with Applications, n/a. doi: 10.10002/nla.674.
9. J. B. ERWAY, R. F. MARCIA, AND J. TYSON, On solving unsymmetric tridiagonal systems without interchanges, Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2010, WCE 2010, 30 June - 2 July, 2010, London, U.K., pp 1887-1892.
10. B. N. PARLETT, D. R. TAYLOR, AND Z. A. LIU, A look-ahead Lánczos algorithm for unsymmetric matrices, Math. Comput., 44, pp. 105-124, 1985.
11. R. E. BANK AND T. F. CHAN, A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems, Numer. Algorithms, 7, pp. 1-16, 1994.
12. A. DAX, Partial pivoting strategies for symmetric gaussian elimination, Math. Program., 22, pp. 288-303, 1982.
13. J. W. H. LIU, A partial pivoting strategy for sparse symmetric matrix decomposition, ACM Trans. Math. Softw., 13, pp. 173-182, 1987.
14. I. S. DHILLON, Reliable computation of the condition number of a tridiagonal matrix in O(n) time, SIAM J. Matrix Anal. Appl., 19, pp. 776-796, 1998.
15. G. I. HARGREAVES, Computing the Condition Number of Tridiagonal and Diagonal-Plus-Semiseparable Matrices in Linear Time, Numerical Analysis Report 447, Manchester Centre for Computational Mathematics, Manchester, 2004.