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Section B

A parallel approach for determining confidence intervals of variable statistics in large and sparse linear equations with RHS ranges

Pages 665-675 | Received 18 Aug 2006, Accepted 17 Sep 2007, Published online: 24 Mar 2009

References

  • Aykanat , C. 1988 . Iterative algorithms for solution of large sparse systems of linear equations on hypercubes . IEEE Trans. Comput. , 37 ( 12 ) : 1554 – 1567 .
  • Balasubramanya Murthy , K. N.B. and Siva Ram Murthy , C. 1996 . Gaussian elimination based algorithm for solving linear equations on mesh connected processors . IEEE Proc. Comp. Digit. Tech. , 143 : 407 – 412 .
  • Basserman , A. 1997 . Parallel sparse matrix computations in iterative solvers on distributed memory machines . J. Parallel Distrib. Comput. , 45 : 46 – 52 .
  • Ben-Asher , Y. and Haber , G. 2004 . Efficient parallel solutions of linear algebraic circuits . J. Parallel Distrib. Comput. , 64 : 163 – 172 .
  • Benzi , M. and Tuma , M. 2002 . A parallel solver for large-scale Markov chain . Appl. Numer. Math. , 41 : 135 – 153 .
  • Borgwardt , K. H. 1986 . The Simplex Method: A Probabilistic Analysis , New York : Springer-Verlag .
  • Catalyurek , U. V. and Aykanat , C. 1999 . Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication . IEEE Trans. Parallel Distributed System , 10 : 673 – 693 .
  • Chandra , R. and Siva Ram Murthy , C. 2003 . A faster algorithm for solving linear algebraic equations on the star graph . J. Parallel Distrib. Comput. , 63 : 465 – 480 .
  • Dantzig , G. B. 1963 . Linear Programming and Extensions , Piscataway, NJ : Princeton University Press .
  • Dekel , E. , Nassimi , D. and Sahni , S. 1981 . Parallel matrix and graph algorithms . SIAM J. Comput. , 10 : 657 – 675 .
  • Farhat , C. and Chen , P. S. 1994 . Tailoring domain decomposition methods for efficient parallel coarse grid solution and for systems with many right hand sides . Contem. Math. , 180 : 401 – 406 .
  • Gallivan , K. , Plemmons , R. J. and Sameh , A. H. 1990 . Parallel algorithms for dense linear algebra computations . SIAM Rev. , 32 : 54 – 135 .
  • Heller , D. 1978 . A survey of parallel algorithms in numerical linear algebra . SIAM Rev. , 20 : 740 – 777 .
  • Hendrickson , B. , Leland , R. and Plimpton , S. 1995 . An efficient parallel algorithm for matrix-vector multiplication . Int. J. High Speed Comput. , 7 : 73 – 88 .
  • Klee , V. and Minty , G. 1972 . How good is the Simplex-Algorithm?, Inequalities III , Edited by: Shisha , O. 159 – 175 . New York : Academic Press .
  • Lindgren , B. W. 1976 . Statistical Theory , 3 , New York : Macmillan .
  • MATLAB manual and instruction sets, The Math Works, Inc. 2000
  • Milosavljevic , I. Z. and Jabri , M. A. 2001 . Experimental evaluation of automatic array alignment in parallelized Matlab . J. Parallel Distrib. Comput. , 61 : 784 – 809 .
  • Ogielski , A. T. and Aiello , W. 1993 . Sparse matrix computation on parallel processor arrays . SIAM J. Scient. Comput. , 14 : 519 – 530 .
  • Ortega , J. 1988 . Introduction to Parallel and Vector Solution of Linear System , New York : Plenum Press .
  • Ortigosa , E. M. , Romero , L. F. and Ramos , J. I. 2003 . Parallel scheduling of the PCG method for banded matrices rising from FDM/FEM . J. Parallel Distrib. Comput. , 63 : 1243 – 1256 .
  • Romero , L. F. and Zapata , E. L. 1995 . Data distribution for sparse matrix vector multiplication . J. Parallel Comput. , 21 : 583 – 605 .
  • Saad , Y. 1996 . Iterative Methods for Sparse Linear Systems , Boston : PWS Publishing Co .
  • Smith , B. , Bjorstad , P. and Gropp , W. 1996 . Domain Decomposition , Cambridge, MA : Cambridge University Press .
  • Stone , H. S. 1973 . An efficient parallel algorithm for the solution of a tridiagonal linear system of equations . J. ACM , 20 : 27 – 38 .
  • Tufo , H. M. and Fischer , P. F. 2001 . Fast parallel direct solvers for coarse grid problems . J. Parallel Distrib. Comput. , 61 : 151 – 177 .
  • Ujaldon , M. U. 1996 . Parallelization techniques for sparse matrix applications . J. Parallel Distrib. Comput. , 38 : 256 – 266 .

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