Parallel solution of sparse linear least squares problems on distributed-memory multiprocessors

Parallel Computing

Volumn 23, Issue 13, 1997, Pages 2075-2093

  Sun, Chunguang ^a  

^a Cornell University ^*  (United States)

Author keywords

Distributed memory multiprocessors; Least squares problems; Multifrontal method; Orthogonal factorization; Parallel algorithms; Sparse matrix; Triangular solution

Indexed keywords

DATA STORAGE EQUIPMENT; DATABASE SYSTEMS; LEAST SQUARES APPROXIMATIONS; PARALLEL ALGORITHMS; PROBLEM SOLVING; STORAGE ALLOCATION (COMPUTER);

DISTRIBUTED MEMORY MULTIPROCESSORS; MULTIFRONTAL METHODS;

PARALLEL PROCESSING SYSTEMS;

EID: 0031383683     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-8191(97)00064-1     Document Type: Article

References (20)

1. R.H. Bisseling, J.G.G. Van De Vorst, Parallel triangular system solving on a mesh network of transputers, SIAM J. Sci. Stat. Comput. 12 (1991) 787-799.
2. A. Björck, Stability analysis of the method of seminormal equations for linear least squares problems, Linear Algebra Appl. 88-89 (1987) 31-48.
3. E. Chu, J.A. George, Sparse orthogonal decomposition on a hypercube multiprocessor, SIAM J. Mat. Anal. Appl. 11 (1990) 453-465.
4. S.C. Eisenstat, M.T. Heath, C.S. Henkel, C.H. Romine, Modified cyclic algorithms for solving triangular systems on distributed-memory multiprocessors, SIAM J. Sci. Stat. Comput. 9 (1988) 589-600.
5. J.A. George, J.W.H. Liu, Householder reflections versus Givens rotations in sparse orthogonal decomposition, Linear Algebra Appl. 88-89 (1987) 223-238.
6. G. Golub, Numerical methods for solving linear least squares problems, Numer. Math. 7 (1965) 206-216.
7. M.T. Heath, Some extensions of an algorithm for sparse linear least squares problems, SIAM J. Sci. Stat. Comput. 3 (1982) 223-237.
8. M.T. Heath, C.H. Romine, Parallel solution of triangular systems on distributed-memory multiprocessors, SIAM J. Sci. Stat. Comput. 9 (1988) 558-588.
9. J.G. Lewis, D.J. Pierce, D.K. Wah, Multifrontal Householder QR factorization, Tech. Report ECATR-127, Boeing Computer Services, Seattle, WA, November 1989.
10. G. Li, T.F. Coleman, A parallel triangular solver for a hypercube multiprocessor, SIAM J. Sci. Stat. Comput. 9 (1988) 485-502.
11. G. Li, T.F. Coleman, A new method for solving triangular systems on distributed-memory message-passing multiprocessors, SIAM J. Sci. Stat. Comput. 10 (1989) 382-396.
12. J.W.H. Liu, On general row merging schemes for sparse Givens transformations, SIAM J. Sci. Stat. Comput. 7 (1986) 1190-1211.
13. J.W.H. Liu, The role of elimination trees in sparse factorization, SIAM J. Mat. Anal. Appl. 11 (1990) 134-172.
14. P. Matstoms, Sparse QR Factorization with Applications to Linear Least Squares Problems, Ph.D. thesis, Linköping University, Sweden, 1994.
15. P.E. Plassmann, Sparse Jacobian estimations factorization on a multiprocessor, in: T.F. Coleman, Y. Li (Eds.), Large-Scale Numerical Optimization, SIAM, Philadelphia, 1990, pp. 152-179.
16. A. Pothen, C. Sun, A mapping algorithm for parallel sparse Cholesky factorization, SIAM J. Sci. Comput. 14 (1993) 1253-1257.
17. C.H. Romine, J.M. Ortega, Parallel solution of triangular systems of equations, Parallel Comput. 6 (1988) 109-114.
18. C. Sun, Efficient parallel solutions of large sparse SPD systems on distributed-memory multiprocessors, Tech. Report CTC92TR102, Advanced Computing Research Institute, Cornell Theory Center, Cornell University, Ithaca, NY, Aug. 1992.
19. C. Sun, Dealing with dense rows in the solution of sparse linear least squares problems, Tech. Report CTC95TR227, Advanced Computing Research Institute, Cornell Theory Center, Cornell University, Ithaca, NY, Dec. 1995.
20. C. Sun, Parallel sparse orthogonal factorization on distributed-memory multiprocessors, SIAM J. Sci. Comput. 17 (1996) 666-685.