Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the stability of relaxed incomplete $ LU$ factorizations

Authors: A. M. Bruaset, A. Tveito and R. Winther
Journal: Math. Comp. 54 (1990), 701-719
MSC: Primary 65F10; Secondary 15A23, 65N20
MathSciNet review: 993924
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: When solving large linear systems of equations arising from the discretization of elliptic boundary value problems, a combination of iterative methods and preconditioners based on incomplete LU factorizations is frequently used. Given a model problem with variable coefficients, we investigate a class of incomplete LU factorizations depending on a relaxation parameter. We show that the associated preconditioner and the factorization itself both are numerically stable. The theoretical results are complemented by numerical experiments.

References [Enhancements On Off] (What's this?)

  • [1] O. Axelsson and V. A. Barker, Finite element solution of boundary value problems. Theory and computation, Academic Press, London, 1984. MR 758437 (85m:65116)
  • [2] O. Axelsson and G. Lindskog, On the eigenvalue distribution of a class of preconditioning methods, Numer. Math. 48 (1986), 479-498. MR 839613 (88a:65037a)
  • [3] -, On the rate of convergence of the preconditioned conjugate gradient method, Numer. Math. 48 (1986), 499-523. MR 839614 (88a:65037b)
  • [4] P. E. BjØrstad and O. B. Widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures, SIAM J. Numer. Anal. 23 (1986), 1097-1120. MR 865945 (88h:65188)
  • [5] J. H. Bramble, J. E. Pasciak, and A. H. Schatz, The construction of preconditioners for elliptic problems by substructuring. I, Math. Comp. 47 (1986), 103-134. MR 842125 (87m:65174)
  • [6] T. Dupont, R. P. Kendall, and H. H. Rachford, Jr., An approximate factorization procedure for solving self-adjoint elliptic difference equations, SIAM J. Numer. Anal. 5 (1968), 559573. MR 0235748 (38:4051)
  • [7] H. C. Elman, A stability analysis of incomplete LU factorizations, Math. Comp. 47 (1986), 191-217. MR 842130 (87h:65057)
  • [8] I. Gustafsson, A class of first order factorization methods, BIT 18 (1978), 142-156. MR 499230 (81j:65057)
  • [9] -, On modified incomplete Cholesky factorization methods for the solution of problems with mixed boundary conditions and problems with discontinuous material coefficients, Internat. J. Numer. Methods Engrg. 14 (1979), 1127-1140. MR 539209 (80h:65092)
  • [10] -, Stability and rate of convergence of modified incomplete Cholesky factorization methods, Ph.D. thesis, Department of Computer Sciences, Chalmers University of Technology and the University of Göteborg, Sweden, 1979. Also available as Research Report 79.02R.
  • [11] J. A. Meijerink and H. A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comp. 31 (1977), 148-162. MR 0438681 (55:11589)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F10, 15A23, 65N20

Retrieve articles in all journals with MSC: 65F10, 15A23, 65N20

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society