On solving unsymmetric tridiagonal systems without interchanges

WCE 2010 - World Congress on Engineering 2010

Volumn 3, Issue , 2010, Pages 1887-1892

  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

BLOCK DIAGONAL; COMPUTATIONAL SAVINGS; DIAGONAL PIVOTING; GAUSSIAN ELIMINATION; ILL-CONDITIONED; NUMERICAL RESULTS; TRIANGULAR MATRICES; TRIDIAGONAL; TRIDIAGONAL SYSTEMS;

LINEAR ALGEBRA; LINEAR SYSTEMS;

ALGORITHMS;

EID: 79959848376     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (11)

1. R. E. BANK AND T. F. CHAN, A composite step biconjugate gradient algorithm for nonsymmetric linear systems, Numer. Algorithms, 7, pp. 1-16, 1994.
2. J. R. BUNCH, Partial pivoting strategies for symmetric matrices, SIAM J. Numer. Anal., 11, pp. 521-528, 1974.
3. J. R. BUNCH AND L. KAUFMAN, Some stable methods for calculating inertia and solving symmetric linear systems, Math. Comp., 31, pp. 163-179, 1977.
4. J. R. BUNCH AND R. F. MARCIA, A pivoting strategy for symmetric tridiagonal matrices, Numer. Linear Algebra Appl., 12, pp. 911-922, 2005.
5. -, A simplified pivoting strategy for symmetric tridiagonal matrices, Numer. Linear Algebra Appl., 13, pp. 865-867, 2006.
6. 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.
7. I. S. DHILLON, Reliable computation of the condition number of a tridiagonal matrix in O(n) time, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 776-796.
8. J. B. ERWAY AND R. F. MARCIA, A backward stability analysis of diagonal pivoting methods for solving unsymmetric tridiagonal systems without interchanges. Accepted for publication in Numerical Linear Algebra with Applications.
9. H. R. FANG AND D. P. O'LEARY, Stable factorizations of symmetric tridiagonal and triadic matrices, SIAM Journal on Matrix Analysis and Applications, 28, pp. 576-595, 2006.
10. 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.
11. 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.