Modified Cholesky algorithms: A catalog with new approaches

Mathematical Programming

Volumn 115, Issue 2, 2008, Pages 319-349

  Fang, Haw Ren ^a   O'Leary, Dianne P ^b  

^a University of Minnesota   (United States)

^b University of Maryland ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE APPLICATIONS; ALGORITHMS; BOOLEAN FUNCTIONS; COMPUTATIONAL METHODS; EVOLUTIONARY ALGORITHMS; FACTORIZATION; MATRIX ALGEBRA; SCHEDULING ALGORITHMS;

(R ,S)-SYMMETRIC; CHOLESKY; CORRECTION MATRIX; INDEFINITE MATRIX; NEW APPROACHES; OPTIMIZ ATION PROBLEMS; POSITIVE DEFINITE MATRICES; SEARCH DIRECTION;

INTEGER PROGRAMMING;

EID: 45149115103     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-007-0177-6     Document Type: Article

References (20)

1. Aasen J.O. (1971). On the reduction of a symmetric matrix to tridiagonal form. BIT 11(3): 233-242
2. Ashaft C., Grimes R.G. and Lewis J.G. (1998). Accurate symmetric indefinite linear equation solvers. SIAM J. Matrix Anal. Appl. 20(2): 513-561
3. Bunch J.R. and Kaufman L. (1977). Some stable methods for calculating inertia and solving symmetric linear systems. Math. Comp. 31: 163-179
4. Bunch J.R. and Parlett B.N. (1971). Direct methods for solving symmetric indefinite systems of linear equations. SIAM J. Numer. Anal. 8(4): 639-655
5. Cheng, S.H.: Symmetric Indefinite Matrices: Linear System Solvers and Modified Inertia Problems. PhD thesis, University of Manchester (1998)
6. Cheng S.H. and Higham N.J. (1998). A modified Cholesky algorithm based on a symmetric indefinite factorization. SIAM J. Matrix Anal. Appl. 19(4): 1097-1110
7. Cuppen J.J.M. (1980). A divide and conquer method for the symmetric tridiagonal eigenproblem. Numer. Math. 36(2): 177-195
8. Demmel, J.W.: Applied Numerical Linear Algebra. SIAM (1997)
9. Fang, H.-r.: Matrix Factorization, Triadic Matrices, and Modified Cholesky Factorizations for Optiimization. PhD thesis, University of Maryland (2006)
10. Fang, H.-r., O'Leary, D.P.: Modified Cholesky algorithms: A catalog with new approaches. Technical Report CS-TR-4807, Computer Science Department, University of Maryland (2006)
11. Fang H.-r. and O'Leary D.P. (2006). Stable factorizations of symmetric tridiagonal and triadic matrices. SIAM J. Matrix Anal. Appl. 28(2): 576-595
12. Forsgren A., Gill P.E. and Murray W. (1995). Computing modified Newton directions using a partial Cholesky factorization. SIAM J. Sci. Comput. 16(1): 139-150
13. Gill P.E. and Murray W. (1974). Newton-type methods for unconstrained and linearly constrained optimization. Math. Program. 28: 311-350
14. Gill P.E., Murray W. and Wright M.H. (1981). Practical Optimization. Academic, New York
15. Horn R.A. and Johnson C.R. (1985). Matrix Analysis. Cambridge University Press, Cambridge
16. Moré J.J. and Sorensen D.C. (1979). On the use of directions of negative curvature in a modified Newton method. Math. Program. 16: 1-20
17. Parlett B.N. and Reid J.K. (1970). On the solution of a system of linear equations whose matrix is symmetric but not definite. BIT 10(3): 386-397
18. Schnabel R.B. and Eskow E. (1990). A new modified Cholesky factorization. SIAM J. Sci. Stat. Comput. 11: 1136-1158
19. Schnabel R.B. and Eskow E. (1999). A revised modified Cholesky factorization algorithm. SIAM J. Optim. 9(4): 1135-1148
20. Stewart G.W. (1980). The efficient generation of random orthogonal matrices with an application to condition estimation. SIAM J. Numer. Anal. 17: 403-409