Low Rank Off-diagonal Block Preconditioners for Solving Sparse Linear Systems on Parallel Computers

  title={Low Rank Off-diagonal Block Preconditioners for Solving Sparse Linear Systems on Parallel Computers},
  author={Randall Bramley},
For a sparse linear system Ax = b, preconditioners of the form C = D + L+ U , where D is the block diagonal part of A (or incomplete factorization approximation of its blocks), and L and U are block strictly lower and upper triangular matrices composed of low-ranks approximations of the respective blocks of A, are examined. C is applied directly, by solving Cz = w, or partially, by applying one step of BSSOR to Cz = w. Use of low-rank approximations of o -diagonal blocks is common in dense… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 12 references

On a family of two{level preconditionings of the incomplete block factorization type

  • A. Yeremin, L. Kolotilina
  • Sov. J. Numer. Anal. Math. Modeling, 1
  • 1986
Highly Influential
20 Excerpts

Ordering schemes for partitioned sparse inverses

  • F. Alvarado
  • SIAM Symposium on Sparse Matrices,
  • 1989
Highly Influential
4 Excerpts

A fast and smoothly converging variant of Bi { CG for the solution of nonsymmetric linear systems

  • H. V. der Vorst, Bi CGSTAB
  • SIAM Journal of Scienti c and Statistical…
  • 1994

User Guide for a Portable Parallel C++ Programming System

  • D. Gannon, S. X. Yang, P. Beckman
  • pC++, Department of Computer Science and CICA…
  • 1994
1 Excerpt

Parallel implementation of preconditioned conjugate gradient methods for solving sparse systems of linear equations

  • E. Anderson
  • Master's thesis, Univ. of Illinois at Urbana…
  • 1988
1 Excerpt

The Computer Solution of Large Sparse Positive De nite Systems

  • A. George, W.-H. Liu
  • Prentice-Hall, Engelwood Cli s, NJ
  • 1981
1 Excerpt

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