Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MODIFLED INCOMPLETE CHOLESKY FACTORIZATION PRECONDITIONERS FOR A SYMMETRIC POSITIVE DEFINITE MATRIX

  • Yun, Jae-Heon (DEPARTMENT OF MATHEMATICS, COLLEGE OF NATURAL SCIENCES, CHUNGBUK NATIONAL UNIVERSITY) ;
  • Han, Yu-Du (DEPARTMENT OF MATHEMATICS, COLLEGE OF NATURAL SCIENCES, CHUNGBUK NATIONAL UNIVERSITY)
  • Published : 2002.08.01
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Abstract

We propose variants of the modified incomplete Cho1esky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

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References

  1. SIAM J. Sci. Stat. Comput. v.6 m-step preconditioned conjugate gradient methods L. Adams https://doi.org/10.1137/0906032
  2. J. Res. Nat. Bur. Stand. v.49 Methods of conjugate gradients for solving linear systems M. R. hestenes;E. L. Stiefel https://doi.org/10.6028/jres.049.044
  3. Lecture Notes Advanced Numerical Analysis F. John
  4. Math. Comp. v.31 An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix J. A. Meijerink;H. A. van der Vorst
  5. Linear Algebra Appl. v.233 A note on comparison theorems for splittings and multisplittings of hermitian positive definite matrices R. Nabben https://doi.org/10.1016/0024-3795(94)00050-6
  6. Introduction to parallel and vector solution of linear systems J. M. Ortega
  7. Linear Algebra Appl. v.48 Regular incomplete factorizations of real positive definite matrices Y. Robert https://doi.org/10.1016/0024-3795(82)90101-X
  8. J. Comput. Appl. Math. v.94 Block incomplete factorization preconditioners for a symmetric block-tridiagonal M-matrix J. H. Yun https://doi.org/10.1016/S0377-0427(98)00078-8

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