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Original Articles

SOLVING SPARSE LEAST SQUARES PROBLEMS WITH PRECONDITIONED CGLS METHOD ON PARALLEL DISTRIBUTED MEMORY COMPUTERS

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Pages 289-305 | Received 11 Mar 1997, Published online: 05 Apr 2007

References

  • S. Ashby . Polynomial preconditioning for conjugate gradient methods , Ph.D. thesis , Department of Computer Science, University of Illinois at Urbana-Champaign , 1987 .
  • Z. Bai , D. Hu , L. Reichel , A Newton basis GMRES implementation. Technical Report 91-03 , University of Kentucky , 1991 .
  • M.W. Berry , R.J. Plemmons . Algorithms and experiments for structural mechanics on high performance architecture. Computer Methods in Applied Mechanics and Engineering , 64 487 – 507 , 1987 .
  • Å. Björck. Numerical Methods for Least Squares Problems , S1AM , Philadelphia , PA , 1995
  • Å. BjörckT. Elfving. Accelerated projection methods for computing pseudoinverse olutions of systems of linear equations. BIT , 19 145 – 163 , 1979 .
  • Å. Björck, T. Elfving , Z. Strakos , Stability of conjugate gradient-type methods for inear least squares problems. Technical Report LiTH-MAT-R-1995-26 , Department of Mathematics , Linköping University , 1994 .
  • I.C. Chio , C.L. Monma , D.F. Shanno , Further development of a primal-dual interior oint method. ORSA Journal on computing , 2 ( 4 ) 304 – 311 , 1990 .
  • A T. Chronopoulos , S.K. Kim , s-Step OTHERQM1N and GMRES implemented on parallel computers. Technical Report 90-R-43 , Supercomputer Institute, University of Minnesota , 1990 .
  • L.G.C. Crone , H.A. van der Vorst , Communication aspects of the conjugate gradient method on distributed memory mechines. Supercomputer , X ( 6 ) 4 – 9 , 1993 .
  • E. de Sturler . A parallel variant of the GMRES(m) . In Proceedings of the 13th IMACS World Congress on Computational and Applied Mathematics. IMACS , Criterion Press , 1991 .
  • E. de Sturler , H.A. van der Vorst , Reducing the effect of the global communication in GMRES(m) and CG on parallel distributed memory computers. Technical Report 832, Mathematical Institute , Universily of Utrecht , Utrecht , The Netherlands , 1994 .
  • J.W. Demmal , M.T. Heath , H.A. van der Vorst , Parallel numerical algebra. Acta Numerca , Cambridge Press , New York , 1993 .
  • J.J. Dongarra , l. S. Duff , D.C. Sorensen , H.A. van der Vorst , Solving Linear Systems on Vector and Shared Memory Computers. SIAM , Philadelphia , PA , 1991 .
  • T Elfving . On lhe conjugate gradient method for solving linear least squares problems. |otTechnical Report LiTH-MAT-R-78-3. Department of Mathematics , Linköping University , 1978 .
  • M. Fortin and R. Glowinski . Augmented Lugrangian Methods: Application to the Numerical Solution of Boundary-value Problems. NH , 1983
  • G.H. Golub , W. Kahan , Calculating the singular values and pseudo-inverse of a matrix. SIAM Journal on Numerical Analysis , 2 205 – 224 . 1965 .
  • M.T. Heath , R.J. Plemmons , R.C. Ward , Sparse orthogonal schemes for structure optimization using the force method. SIAM Journal on Scientific and Statistical Computing , 5 ( 3 ) 514 – 532 , 1984 .
  • M.R , Hestenes E. Stiefel . Methods of conjugate gradients for solving linear system. J. Res. Nal. Bur. Stds. B , 49 409 – 436 , 1952 .
  • A. Jennings and M.A . Ajiz .: Incomplete methods for solving ATAx =b. SIAM Journal on Scientific and Statistical Computing , 5 : 978 – 987 , 1984 .
  • J.A. Meijerink , H.A. van der Vorst , An iterative solution method for linear system of which the coefficient matrix is a symmetric M-matrix. Mathematics of Computation , 31 ( 137 ) 148 – 162 , 1977 .
  • C.C , Paige M.A. Saunders .LSQR An algorithm for sparse linear equations and sparse least squares. ACM Transactions on Mathematical Software , 8 43 – 71 , 1982 .
  • C. Pommerell . Solution of large unsymmetric systems of linear equations. Ph.D. thesis , ETH , 1992 .
  • X. Wang . Incomplete factorization preconditioning for linear least squares problems. Ph.D. thesis , Department of Computer Science, University of Illinois at Urbana-Champaign , 1993 .
  • T. Yang . Error analysis for incomplete modified Gram-Schmidt preconditioner. In Proceedings of Prague Mathematical Conference (PMC-96) , July 1996 . Mathematical Institute of Academy Sciencesn, Zitza 25 , CZ-l 15 67 Praha , Czech Republic
  • T. Yang . Iterative methods for least squares and total least squares problems. Licentiate Thesis LiU-TEK-LIC-199625 , 1996 . Linköping University , 581 83 , Linköping , Sweden .

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