Simultaneous backward stability of Gauss and Gauss-Jordan elimination

Numerical Linear Algebra with Applications

Volumn 10, Issue 4, 2003, Pages 317-321

  Pena J M ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Backward error; Gauss elimination; Gauss Jordan elimination; Growth factor; Pivoting; Stability

Indexed keywords

EID: 0142055265     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.299     Document Type: Article

References (9)

1. Peters G, Wilkinson JH. On the stability of Gauss-Jordan elimination with pivoting. Communications of the Association for Computing Machinery 1975; 18:20-24.
2. Higham NJ. Accuracy and Stability of Numerical Algorithms. SIAM: Philadelphia, 1996.
3. Malyshev AN. A note on the stability of Gauss-Jordan elimination for diagonally dominant matrices. Computing 2000; 65:281-284.
4. Poole G, Neal L. The rook's pivoting strategy. Journal of Computational and Applied Mathematics 2000; 123:353-369.
5. Dekker TJ, Hoffmann W. Rehabilitation of the Gauss-Jordan algorithm. Numerische Mathematik 1989; 54:591-599.
6. Peña JM. Pivoting strategies leading to diagonal dominance by rows. Numerische Mathematik 1998; 81:293-304.
7. Trefethen LN, Schreiber RS. Average case stability of Gaussian elimination. SIAM Journal on Matrix Analysis and Applications 1990; 11:335-360.
8. Businger PA. Monitoring the numerical stability of Gaussian elimination. Numerische Mathematik 1971; 16:360-361.
9. Foster LV. The growth factor and efficiency of Gaussian elimination with rook pivoting. Journal of Computational and Applied Mathematics 1997; 86:177-194.