Modifying a sparse cholesky factorization

SIAM Journal on Matrix Analysis and Applications

Volumn 20, Issue 3, 1999, Pages 606-627

  Davis, Timothy A ^a   Hager, William W ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

Cholesky factorization; Direct methods; Mathematical software; Matrix updates; Numerical linear algebra; Sparse matrices

Indexed keywords

EID: 0033239801     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479897321076     Document Type: Article

References (36)

1. P. R. AMESTOY, T. A. DAVIS, AND I. S. DUFF, An approximate minimum degree ordering algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 886-905.
2. R. H. BARTELS, G. H. GOLUB, AND M. A. SAUNDERS, Numerical techniques in mathematical programming, in Nonlinear Programming, J. B. Rosen, O. L. Mangasarian, and K. Ritter, eds., Academic Press, New York, 1970, pp. 123-176.
3. J. M. BENNETT, Triangular factors of modified matrices, Numer. Math., 7 (1965), pp. 217-221.
4. C. H. BISCHOF, G.-T. PAN, AND P. T. P. TANG, A Cholesky up- and downdating algorithm for systolic and SIMD architectures, SIAM J. Sci. Comput., 14 (1993), pp. 670-676.
5. N. A. CARLSON, Fast triangular factorization of the square root filter, AIIA J., 11 (1973), pp. 1259-1265.
6. S. M. CHAN AND V. BRANDWAJN, Partial matrix refactorization, IEEE Trans. on Power Systems, PWRS-1 (1986), pp. 193-200.
7. T. H. CORMEN, C. E. LEISERSON, AND R. L. RIVEST, Introduction to Algorithms, The MIT Electrical Engineering and Computer Science Series. MIT Press, Cambridge, MA; McGraw-Hill, New York, 1990.
8. J. J. DONGARRA AND E. GROSSE, Distribution of mathematical software via electronic mail, Comm. ACM, 30 (1987), pp. 403-407.
9. I. S. DUFF, A. M. ERISMAN, AND J. K. REID, Direct Methods for Sparse Matrices, Oxford University Press, London, 1986.
10. S. C. EISENSTAT, M. C. GURSKY, M. H. SCHULTZ, AND A. H. SHERMAN, Yale sparse matrix package, I: The symmetric codes, Internat. J. Numer. Methods Engrg., 18 (1982), pp. 1145-1151.
11. A. GEORGE AND J. W. H. LIU, The design of a user interface for a sparse matrix package, ACM Trans. Math. Software, 5 (1979), pp. 139-162.
12. A. GEORGE AND J. W. H. LIU, An optimal algorithm for symbolic factorization of symmetric matrices, SIAM J. Comput., 9 (1980), pp. 583-593.
13. A. GEORGE AND J. W. H. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
14. A. GEORGE, J. LIU, AND E. NG, A data structure for sparse QR and LU factorizations, SIAM J. Sci. Stat. Comput., 9 (1988). pp. 100-121.
15. J. R. GILBERT, Predicting Structure in Sparse Matrix Computations, Tech. report CS-86-750, Computer Science Dept., Cornell Univ., Ithaca, NY, 1986.
16. J. R. GILBERT, Predicting structure in sparse, matrix computations, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 62-79.
17. J. R. GILBERT, C. MOLER, AND R. SCHREIBER, Sparse matrices in MATLAB: Design and implementation, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 333-356.
18. J. R. GILBERT, E. G. NG, AND B. W. PEYTON, An efficient algorithm to compute row and column counts for sparse Cholesky factorization, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1075-1091.
19. J. R. GILBERT AND T. PEIERLS, Sparse partial pivoting in time proportional to arithmetic operations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 862-874.
20. P. E. GILL, G. H. GOLUB, W. MURRAY, AND M. A. SAUNDERS, Methods for modifying matrix factorizations, Math. Comp., 28 (1974), pp. 505-535.
21. P. E. GILL AND W. MURRAY, Quasi-Newton methods for unconstrained optimization, J. Inst. Math. Appl., 9 (1972), pp. 91-108.
22. P. E. GILL, W. MURRAY, AND M. A. SAUNDERS, Methods for computing and modifying the LDV factors of a matrix, Math. Comp., 29 (1975), pp. 1051-1077.
23. W. W. HAGER, Condition estimates, SIAM J. Sci. Stat. Comput., 5 (1984), pp. 311-316.
24. W. W. HAGER, Applied Numerical Linear Algebra, Prentice-Hall, Englewood Cliffs, NJ, 1988.
25. W. W. HAGER, Updating the inverse of a matrix, SIAM Rev., 31 (1989), pp. 221-239.
26. W. W. HAGER, The LP dual active set algorithm, in High Performance Algorithms and Software in Nonlinear Optimization, R. De Leone, A. Murli, P. M. Pardalos, and G. Toraldo, eds., Kluwer Academic Publishers, Norwell, MA, to appear.
27. K. H. LAW, Sparse matrix factor modification in structural reanalysis, Internat. J. Numer. Methods Engrg., 21 (1985), pp. 37-63.
28. K. H. LAW, On updating the structure of sparse matrix factors, Internat. J. Numer. Methods Engrg., 28 (1989), pp. 2339-2360.
29. J. W. H. LIU, The role of elimination trees in sparse factorization, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 134-172.
30. C.-T. PAN, A modification to the UNPACK downdating algorithm, BIT, 30 (1990), pp. 707-722.
31. D. J. ROSE, R. E. TARJAN, AND G. S. LUEKER, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5 (1976), pp. 266-283.
32. D. G. Row, G. H. POWELL, AND D. P. MONDKAR, Solution of progressively changing equilibrium equations for nonlinear structures, Comput. & Structures, 7 (1977), pp. 659-665.
33. R. SCHREIBER, A new implementation of sparse Gaussian elimination, ACM Trans. Math. Software, 8 (1982), pp. 256-276.
34. A. H. SHERMAN, On the Efficient Solution of Sparse Systems of Linear and Nonlinear Equations, Tech. report 46, Dept. of Computer Science, Yale Univ., New Haven, CT, 1975.
35. G. STRANG, Linear Algebra and Its Applications, Academic Press, New York, 1980.
36. J. H. WILKINSON, Linear algebra algorithms, in Software for Numerical Mathematics, Proceedings of the Loughborough Univ. of Technology Conf. of the Inst. of Mathematics and its Appl., 1973, D. J. Evans, ed., Academic Press, New York, 1974, pp. 17-28.