Structured backward errors for KKT systems

Linear Algebra and Its Applications

Volumn 288, Issue 1-3, 1999, Pages 75-88

  Sun, Ji Guang ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

KKT systems; Normwise backward error; Strong stability

Indexed keywords

EID: 0039035736     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)10184-2     Document Type: Article

References (18)

1. Å. Björck, Numerical stability of methods for solving augmented systems, Contemporary Mathematics 204 (1997) 51-60.
2. Å. Björck, C.C. Paige, Solution of augmented linear systems using orthogonal factorizations, BIT 34 (1994) 1-24.
3. J.R. Bunch, The weak and strong stability of algorithms in numerical linear algebra, Linear Algebra Appl. 88/89 (1987) 49-66.
4. J.R. Bunch, J.W. Demmel, C.F. Van Loan, The strong stability of algorithms for solving symmetric linear systems, SIAM J. Matrix Anal. Appl. 10 (1989) 494-499.
5. T.F. Coleman, Large Sparse Numerical Optimization, Lecture Notes in Computer Science, vol. 165, Springer, Berlin, 1984.
6. R. Fletcher, Practical Methods of Optimization, 2nd ed., Chichester, UK, 1987.
7. R. Fletcher, T. Johnson, On the stability of null-space methods for KKT systems, SIAM J. Matrix Anal. Appl. 18 (1997) 938-958.
8. E. Galligani, L. Zanni, Error analysis of an algorithm for equality-constrained quadratic programming problems, Computing 58 (1997) 47-67.
9. G.H. Golub, C.F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
10. D.J. Higham, N.J. Higham, Backward error and condition of structured linear systems, SIAM J. Matrix Anal. Appl. 13 (1992) 162-175.
11. N.J. Higham, Accuracy and Stability of Numerical Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1996.
12. N.J. Higham, S.H. Cheng, Modifying the inertia of matrices arising in optimization, Numerical Analysis Report No. 295, Manchester Center for Computational Mathematics, Manchester, UK, September 1996, to appear in Linear Algebra Appl.
13. J.L. Rigal, J. Gaches, On the compatibility of a given solution with the data of a linear system, J. Assoc. Comput. Mach. 14 (1967) 543-548.
14. G.W. Stewart, J.-G. Sun, Matrix Perturbation Theory, Academic Press, New York, 1990.
15. G. Strang, A framework for equilibrium equations, SIAM Rev. 30 (1988) 283-297.
16. J.-G. Sun, Backward perturbation analysis of certain characteristic subspaces, Numer. Math. 65 (1993) 357-382.
17. J.-G. Sun, Optimal backward perturbation bounds for linear systems and linear least squares problems, UMINF 96.15, ISSN-0348-0542, Department of Computing Science, Umeå University, 1996.
18. J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford, 1965.