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SEMI-CONVERGENCE OF THE PARAMETERIZED INEXACT UZAWA METHOD FOR SINGULAR SADDLE POINT PROBLEMS

윤재헌
대한수학회 (The Korean Mathematical Society)|2015.09|대한수학회보 (Bulletin of the KMS)|제52권 제5호|pp. 1669-1681

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참고문헌

키워드

iterative methodMoore-Penrose inversesingular saddle point problemUzawa methodsemi-convergence
주제분류수학

초록

In this paper, we provide semi-convergence results of the parameterized inexact Uzawa method with singular preconditioners for solving singular saddle point problems. We also provide numerical experiments to examine the effectiveness of the parameterized inexact Uzawa method with singular preconditioners.

Abstract

In this paper, we provide semi-convergence results of the parameterized inexact Uzawa method with singular preconditioners for solving singular saddle point problems. We also provide numerical experiments to examine the effectiveness of the parameterized inexact Uzawa method with singular preconditioners.

참고문헌 (22)

  1. M. Arioli, "On the augmented system approach to sparse least squares problems", Numer. Math, 55(6), pp.667~684 (1989)
  2. Z. Z. Bai, "On generalized successive overrelaxation methods for augmented linear systems", Numer. Math, 102(1), pp.1~38 (2005)
  3. Z. Z. Bai, "On parameterized inexact Uzawa methods for generalized saddle point problems", Linear Algebra Appl, 428(11-12), pp.2900~2932 (2008)
  4. A. Berman, "Nonnegative Matrices in the Mathematical Sciences" (1979), Academic Press
  5. Z. H. Cao, "On the convergence of general stationary linear iterative methods for singular linear systems", SIAM J. Matrix Anal. Appl, 29, pp.1382~1388 (2007)
  6. Z. Chao, "Semi-convergence analysis of the Uzawa-SOR methods for sin-gular saddle point problems", Appl. Math. Lett, 35, pp.52~57 (2014)
  7. Z. Chao, "Optimal parameters of the generalized symmetric SOR method for augmented systems", J. Comput. Appl. Math, 266, pp.52~60 (2014)
  8. M. T. Darvishi, "Symmetric SOR method for augmented systems", Appl. Math. Comput, 183(1), pp.409~415 (2006)
  9. H. C. Elman, "Preconditioning for the steady-state Navier-Stokes equations with low viscosity", SIAM J. Sci. Comput, 20(4), pp.1299~1316 (1999)
  10. H. C. Elman, "Fast nonsymmetric iteration and preconditioning for Navier-Stokes equations", SIAM J. Sci. Comput, 17(1), pp.33~46 (1996)
  11. G. H. Golub, "SOR-like methods for augmented systems", BIT, 41(1), pp.71~85 (2001)
  12. F. H. Harlow, "Numerical calculation of time-dependent viscous incom-pressible flow of fluid with free surface", Phys. Fluids, 8, pp.2182~2189 (1965)
  13. J. I. Li, "The semi-convergence of generalized SSOR method for singular augmented systems, High Performance Computing and Applications", Lecture Notes in Computer Science, 5938, pp.230~235 (2010)
  14. S. Wright, "Stability of augmented system factorization in interior point methods", SIAM J. Matrix Anal. Appl, 18(1), pp.191~222 (1997)
  15. J. Y. Yuan, "Preconditioned conjugate gradient methods for generalized least squares problem", J. Comput. Appl. Math, 71(2), pp.287~297 (1996)
  16. J. H. Yun, "Variants of the Uzawa method for saddle point problem", Comput. Math. Appl, 65(7), pp.1037~1046 (2013)
  17. J. H. Yun, "Convergence of relaxation iterative methods for saddle point problem", Appl. Math. Comput, 251, pp.65~80 (2015)
  18. G. F. Zhang, "On generalized symmetric SOR method for augmented systems", J. Comput. Appl. Math, 219(1), pp.51~58 (2008)
  19. G. F. Zhang, "A generalization of parameterized inexact Uzawa method for singular saddle point problems", Appl. Math. Comput, 219(9), pp.4225~4231 (2013)
  20. N. Zhang, "On the convergence of general stationary iterative methods for range-Hermitian singular linear systems", Numer. Linear Algebra Appl, 17(1), pp.139~154 (2010)
  21. B. Zheng, "On semi-convergence of parameterized Uzawa methods for singular saddle point problems", Linear Algebra Appl, 431(5-7), pp.808~817 (2009)
  22. L. Zhou, "Semi-convergence analysis of GMSSOR methods for singular saddle point problems", Comput. Math. Appl, 68(5), pp.596~605 (2014)

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