DRIC: A dynamic version of the RIC method.A new incomplete factorization method is proposed, differing from previous ones by the way in which the diagonal entries of the triangular factors are defined. A comparison is given with the dynamic modified incomplete factorization methods of O. Axelsson and V. A. Barker [Finite element solution of boundary value problems. Theory and computation (1984; Zbl 0537.65072)] and R. Beauwens [Lect. Notes Math. 1457, 1-16 (1990; Zbl 0713.65026)] and with the relaxed incomplete Cholesky (RIC) method of O. Axelsson and G. Lindskog [Numer. Math. 48, 479-498 (1986; Zbl 0564.65016)]. Theoretical arguments show that the new method is at least as robust as both previous ones, while numerical experiments made in the context of discrete partial differential equations show an effective improvement in many practical circumstances, particularly for anisotropic problems.

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  1. Osei-Kuffuor, Daniel; Li, Ruipeng; Saad, Yousef: Matrix reordering using multilevel graph coarsening for ILU preconditioning (2015)
  2. Maclachlan, S.; Osei-Kuffuor, D.; Saad, Yousef: Modification and compensation strategies for threshold-based incomplete factorizations (2012)
  3. Gu, Ming; Li, Xiaoye S.; Vassilevski, Panayot S.: Direction-preserving and Schur-monotonic semiseparable approximations of symmetric positive definite matrices (2010)
  4. Niu, Qiang; Grigori, Laura; Kumar, Pawan; Nataf, Frédéric: Modified tangential frequency filtering decomposition and its Fourier analysis (2010)
  5. Niu, Qiang; Lu, Lin-Zhang: Fourier analysis of frequency filtering decomposition preconditioners (2010)
  6. Larin, M.; Il’in, Valeriĭ Pavlovich: Variable-step preconditioned conjugate gradient method for partial symmetric eigenvalue problems (2005)
  7. van der Vorst, Henk A.: Efficient and reliable iterative methods for linear systems (2002)
  8. Arany, I.: Numerical experiences of solving elasticity systems by PCG methods. (2001)
  9. Magolu monga Made, M.; van der Vorst, H.A.: Parallel incomplete factorizations with pseudo-overlapped subdomains (2001)
  10. Milyukova, O.Y.: Parallel approximate factorization method for solving discrete elliptic equations (2001)
  11. Milyukova, O.Yu.: A parallel iterative method with a factorized preconditioning matrix for elliptic equations (2000)
  12. Saad, Yousef; van der Vorst, Henk A.: Iterative solution of linear systems in the 20th century (2000)
  13. Arany, I.: Solving systems of elastic bar structures by preconditioned conjugate gradient method (1999)
  14. Beauwens, Robert: Implementation strategies for block recursive factorizations (1999)
  15. Botta, E.F.F.; Wubs, F.W.: Matrix renumbering ILU: An effective algebraic multilevel ILU preconditioner for sparse matrices (1999)
  16. Saint-Georges, Pascal; Warzee, Guy; Notay, Yvan; Beauwens, Robert: Problem-dependent preconditioners for iterative solvers in FE elastostatics (1999)
  17. Vuik, C.; Segal, A.; Meijerink, J.A.: An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients (1999)
  18. Dongarra, Jack J.; Duff, Iain S.; Sorensen, Danny C.; Van der Vorst, Henk A.: Numerical linear algebra for high-performance computers (1998)
  19. Botta, E.F.F.; Dekker, K.; Notay, Y.; van der Ploeg, A.; Vuik, C.; Wubs, F.W.; de Zeeuw, P.M.: How fast the Laplace equation was solved in 1995 (1997)
  20. Gustafsson, Ivar: An incomplete factorization preconditioning method based on modification of element matrices (1996)

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