A software package for sparse orthogonal factorization and updating

ACM Transactions on Mathematical Software

Volumn 28, Issue 4, 2002, Pages 448-482

  Edlund, Ove ^a  

^a LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Algorithms; Downdating; G.1.3 Numerical Analysis : Numerical Linear Algebra sparse, structured, and very large systems; G.4 Mathematics of Computing : Mathematical Software; Orthogonal factorization; Software; Sparse matrix; Updating

Indexed keywords

EID: 0039488522     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/592843.592848     Document Type: Article

References (25)

1. ADLERS, M. 2000. PhD Dissertation. PhD Thesis, Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden.
2. AMESTOY, P., DAVIS, T. A., AND DUFF, I. S. 1996. An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17, 4, 886-905.
3. BJÖRK, Å. 1987. Stability analysis of the method of semi-normal equations for least squares problems. Linear Algebra Appl. 88/89, 31-48.
4. COLEMAN, T. F., EDENBRANDT, A., AND GILBERT, J. R. 1986. Predicting fill for sparse orthogonal factorization. J. ACM 33, 3, 517-532.
5. DAVIS, T. A. AND HAGER, W. W. 1999. Modifying a sparse Cholesky factorization. SIAM J. Matrix Anal. Appl. 20, 3, 606-627.
6. DAVIS, T. A. AND HAGER, W. W. 2001. Multiple-rank modifications of a sparse Cholesky factorization. SIAM J. Matrix Anal. Appl. 22, 4, 997-1013.
7. DUFF, I. S. 1981. On algorithms for obtaining a maximum traversal. ACM Trans. Math. Softw. 7, 3, 315-330.
8. 1/2τ) assignment algorithms. ACM Trans. Math. Softw. 14, 3, 267-287.
9. DUFF, I. S., ERISMAN, A. M., AND REID, J. K. 1986. Direct Methods for Sparse Matrices. Oxford University Press, New York.
10. EDLUND, O., MADSEN, K., AND NIELSEN, H. B. 1999. A piecewise quadratic approach for solving sparse linear programming problems (to be submitted).
11. GEORGE, A. AND LIU, J. W. H. 1989. The evolution of the minimum degree ordering algorithm. SIAM Rev. 31, 1, 1-19.
12. GILBERT, J. R., MOLER, C., AND SCHREIBER, R. 1992. Sparse matrices in Matlab: Design and implementation. SIAM J. Matrix Anal. Appl. 13, 1, 609-629.
13. GILL, P. E. AND MURRAY, W. 1973. A numerically stable form of the simplex method. Linear Algebra Appl. 7, 99-138.
14. GOLUB, G. H. AND VAN LOAN, C. F. 1989. Matrix Computations, second ed. Johns Hopkins University Press, Baltimore.
15. 5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2, 225-231.
16. LARIMORE, S. I. 1998. An approximate minimum degree column ordering algorithm. CISE Tech Rep. TR-98-016, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, Fla. MS Thesis.
17. MADSEN, K. AND NIELSEN, H. B. 1990. Finite algorithms for robust linear regression. BIT 30, 333-356.
18. 1 estimation. SIAM J. Optim. 3, 2, 223-235.
19. MADSEN, K., NIELSEN, H. B., AND PINAR, M. Ç. 1996. A new finite continuation algonthm for linear programming. SIAM J. Optim. 6, 3, 600-616.
20. MATSTOMS, P. 1994. Sparse QR factorization with applications to linear least squares problems. PhD Thesis, Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden.
21. MATSTOMS, P. 1997. Sparse linear least squares problems in optimization. Comput. Optim. Appl. 7, 1, 89-110.
22. TAx = c. Tech. Rep. NI-90-01, Institute for Numerical Analysis, Technical University of Denmark, Lyngby 2800, Denmark.
23. PINAR, M. Ç. 1997. Piecewise-linear pathways to the optimal set in linear programming. J. Optim. Theor. Appl. 93, 619-634.
24. POTHEN, A. AND FAN, C.-J. 1990. Computing the block triangular form of a sparse matrix. ACM Trans. Math. Softw. 16, 4, 303-324.
25. SAUNDERS, M. A. 1972. Large-scale linear programming using the Cholesky factorization. Tech. Rep. STAN-CS-72-252, Computer Science Dept, Stanford University, Stanford, CA.