Solution of large-scale weighted least-squares problems

Numerical Linear Algebra with Applications

Volumn 9, Issue 2, 2002, Pages 93-106

  Baryamureeba, Venansius ^a  

^a MAKERERE UNIVERSITY   (Uganda)

Author keywords

Conjugate gradients; Dense columns; Least squares; Preconditioner

Indexed keywords

EID: 0036109253     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.232     Document Type: Article

References (19)

1. Hu TC, Shing MT. In A Decomposition Algorithm for Circuit Routing, Hu TC, Kuh ES. (eds.).
2. Vannelli A. An adaptation of the interior point method for solving the global routing problem. IEEE Transactions on CAD 1991; 10:193-203.
3. Vannelli A. An efficient linear programming based approach for finding netlist partitions. Proceedings Can. Conference VLSI, 1988.
4. Weis BX, Mlynski DA. A new relative placement procedure based on MSST and linear programming. Proceedings of the IEEE International Symposium on Circuits & Systems (ISCAS), 1987; 564-567.
5. Adler I, Karmarkar N, Resende MGC, Viega G. An implementation of Karmarkars's algorithm for linear programming. Mathematical Programming 1989; 44:297-336.
6. Gill PE, Murray W, Saunders MA, Tomlin JA, Wright MH. On projected Newton methods for linear programming and equivalence to Karmarkar's projective method. Mathematical Programming 1986; 36:183-209.
7. Gill PE, Murray W, Saunders MA. A single-phase dual barrier method for linear programming. Report SOR 88-10, Systems Optimization, Laboratory, Stanford University, Stanford, CA.
8. Baryamureeba V, Steihaug T, Zhang Y. Properties of a class of preconditioners for weighted least squares problems. Technical Report No. 170, Department of Informatics, University of Bergen, 5020 Bergen, Norway, April 30, 1999 (Revised July 6, 1999).
9. Wang W, O'Leary DP. Adaptive use of iterative methods in interior point methods for linear programming. Computer Science Department Report CS-TR-3560, University of Maryland, November 1995.
10. Wang W, O'Leary DP. Adaptive use of iterative methods in predictor-corrector interior point methods for linear programming. Technical Report No. CS-TR-4011, Computer Science Department, University of Maryland, April 1999.
11. Wilkinson JH. The Eigenvalue Problem. Oxford University Press: London, 1965.
12. Björck Å. Numerical Methods for Least Squares Problems. ISBN 0-89871-360-9. SIAM: Philadelphia, PA, 1996.
13. Zhang Y. Solving large scale linear programs by interior point methods under the MATLAB environment. Optimization Methods and Software 1998; 10:1-31.
14. Andersen KD. A modified Schur-complement method for handling dense columns in interior point methods for linear programming. ACM Transactions on Mathematical Software 1996; 22:348-356.
15. Bartels R, Kaufman L. Cholesky factor updating techniques for rank 2 matrix modifications. SIAM Journal on Matrix Analysis and Applications 1989; 10:557-592.
16. Baryamureeba V, Steihaug T. Computational issues for a new class of preconditioners. In Large-Scale Scientific Computations of Engineering and Environmental Problems II, Griebel M, Margenov S, Yalamov P. (eds.), In Notes on Numerical Fluid Mechanics, vol. 73, Vieweg: Braunschweig, 2000; 128-135.
17. Davis TA, Hager WW. Modifying a sparse Cholesky factorization. SIAM Journal on Matrix Analysis and Applications (Electronic Edition). 1999; 20:606-627.
18. Gill PE, Golub GH, Murray W, Saunders MA. Methods for modifying matrix factorizations. Mathematics of Computation 1974; 28:505-535.
19. Gay DM. Electronic mail distribution of linear programming test problems. Mathematical Programming Society COAL Newsletter 1985; (13): 10-12.