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Volumn 77, Issue 262, 2008, Pages 831-850

A sharp convergence estimate for the method of subspace corrections for singular systems of equations

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EID: 42349093616     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-07-02052-2     Document Type: Article
Times cited : (29)

References (29)
  • 1
    • 0031076132 scopus 로고    scopus 로고
    • The partition of unity method
    • MR1429534 97j:73071
    • I. Babuška and J. M. Melenk. The partition of unity method. Internat. J. Numer. Methods Engrg., 40(4):727-758, 1997. MR1429534 (97j:73071)
    • (1997) Internat. J. Numer. Methods Engrg , vol.40 , Issue.4 , pp. 727-758
    • Babuška, I.1    Melenk, J.M.2
  • 2
    • 42349092387 scopus 로고    scopus 로고
    • A. B. Berman and R. J. Plemmons. Nonnegative matrices in the mathematical sciences. SIAM classics in Applied Mathematics, Philadelphia, 1994. MR1298430 (95e:15013)
    • A. B. Berman and R. J. Plemmons. Nonnegative matrices in the mathematical sciences. SIAM classics in Applied Mathematics, Philadelphia, 1994. MR1298430 (95e:15013)
  • 3
    • 17444403192 scopus 로고    scopus 로고
    • On the finite element solution of the pure Neumann problem
    • 50-66 (electronic, MR2149101 2007a:65185
    • Pavel Bochev and R. B. Lehoucq. On the finite element solution of the pure Neumann problem. SIAM Rev., 47(1):50-66 (electronic), 2005. MR2149101 (2007a:65185)
    • (2005) SIAM Rev , vol.47 , Issue.1
    • Bochev, P.1    Lehoucq, R.B.2
  • 4
    • 67649463901 scopus 로고    scopus 로고
    • The analysis of multigrid methods
    • North-Holland, Amsterdam, MR1804746 2001m:65183
    • J. H. Bramble and X. Zhang. The analysis of multigrid methods. Handbook of numerical analysis, Vol. VII. North-Holland, Amsterdam, 2000. MR1804746 (2001m:65183)
    • (2000) Handbook of numerical analysis , vol.7
    • Bramble, J.H.1    Zhang, X.2
  • 5
    • 0030783493 scopus 로고    scopus 로고
    • Iterative techniques for time dependent stokes problems
    • MR1442058 98e:65091
    • J. H. Bramble and J. E. Pasciak. Iterative techniques for time dependent stokes problems. Comput. Math. with Appl., 33:13-30, 1997. MR1442058 (98e:65091)
    • (1997) Comput. Math. with Appl , vol.33 , pp. 13-30
    • Bramble, J.H.1    Pasciak, J.E.2
  • 6
    • 0035604369 scopus 로고    scopus 로고
    • A note on properties of splittings of singular symmetric positive semidefinite matrices
    • MR1836872 2002b:65045
    • Z. H. Cao. A note on properties of splittings of singular symmetric positive semidefinite matrices. Numer. Math., 88:603-606, 2001. MR1836872 (2002b:65045)
    • (2001) Numer. Math , vol.88 , pp. 603-606
    • Cao, Z.H.1
  • 7
    • 8644260616 scopus 로고    scopus 로고
    • Best approximation in inner product spaces
    • Springer-Verlag, New York, MR1823556 2002c:41001
    • Frank Deutsch. Best approximation in inner product spaces. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 7. Springer-Verlag, New York, 2001. MR1823556 (2002c:41001)
    • (2001) CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC , vol.7
    • Deutsch, F.1
  • 9
    • 0003360974 scopus 로고
    • Multigrid methods and applications
    • of, Springer-Verlag, Berlin, MR814495 87e:65082
    • Wolfgang Hackbusch. Multigrid methods and applications, volume 4 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 1985. MR814495 (87e:65082)
    • (1985) Springer Series in Computational Mathematics , vol.4
    • Hackbusch, W.1
  • 10
    • 0001457518 scopus 로고
    • On the solution of singular and semidefinite linear systems by iteration
    • MR0195244 33:3447
    • H. B. Keller. On the solution of singular and semidefinite linear systems by iteration. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2:281-290, 1965. MR0195244 (33:3447)
    • (1965) J. Soc. Indust. Appl. Math. Ser. B Numer. Anal , vol.2 , pp. 281-290
    • Keller, H.B.1
  • 11
    • 34547210117 scopus 로고    scopus 로고
    • On the convergence of iterative methods for semidefinite linear systems
    • MR2262973
    • Young-Ju Lee, Jinbiao Wu, Jinchao Xu, and Ludmil Zikatanov. On the convergence of iterative methods for semidefinite linear systems. SIAM Journal on Matrix Analysis and Applications., 28 (3): 634-641, 2006. MR2262973
    • (2006) SIAM Journal on Matrix Analysis and Applications , vol.28 , Issue.3 , pp. 634-641
    • Lee, Y.-J.1    Wu, J.2    Xu, J.3    Zikatanov, L.4
  • 12
    • 0034414037 scopus 로고    scopus 로고
    • Comparison theorems for the convergence factor of iterative methods for singular matrices
    • MR1782417 2001h:65040
    • I. Marek and D. B. Szyld. Comparison theorems for the convergence factor of iterative methods for singular matrices. Linear Algebra and its Applications., 316:67-87, 2000. MR1782417 (2001h:65040)
    • (2000) Linear Algebra and its Applications , vol.316 , pp. 67-87
    • Marek, I.1    Szyld, D.B.2
  • 13
    • 2942615438 scopus 로고    scopus 로고
    • I. Marek and D. B. Szyld. Algebraic Schwarz methods for the numerical solution of Markov chains. Linear Algebra and its Applications., 386:67-81 Sp. Iss. SI, 2004. MR2066608 (2005i:60005)
    • I. Marek and D. B. Szyld. Algebraic Schwarz methods for the numerical solution of Markov chains. Linear Algebra and its Applications., 386:67-81 Sp. Iss. SI, 2004. MR2066608 (2005i:60005)
  • 14
    • 37849031437 scopus 로고    scopus 로고
    • Schwarz iterations for symmetric positive semidefinite problems
    • MR2288016
    • R. Nabben and D. B. Szyld. Schwarz iterations for symmetric positive semidefinite problems. SIAM J. Matrix Anal. Appl., 29:98-116. MR2288016
    • SIAM J. Matrix Anal. Appl , vol.29 , pp. 98-116
    • Nabben, R.1    Szyld, D.B.2
  • 15
    • 42349085834 scopus 로고    scopus 로고
    • S. V. Nepomnyaschikh. Schwartz alternating method for solving the singular Neumann problem [translation of computational algorithms in problems of mathematical physics (Russian), 99-112, Akad. Nauk SSSR Sibirsk, Otdel., Vychisl. Tsentr, Novosibirsk, 1985].
    • S. V. Nepomnyaschikh. Schwartz alternating method for solving the singular Neumann problem [translation of computational algorithms in problems of mathematical physics (Russian), 99-112, Akad. Nauk SSSR Sibirsk, Otdel., Vychisl. Tsentr, Novosibirsk, 1985].
  • 16
    • 42349086008 scopus 로고
    • Soviet Journal of Numerical Analysis and Mathematical Modelling. MR1124937 92k:65182
    • Soviet J. Numer. Anal. Math. Modelling, 5(1):69-78, 1990. Soviet Journal of Numerical Analysis and Mathematical Modelling. MR1124937 (92k:65182)
    • (1990) Soviet J. Numer. Anal. Math. Modelling , vol.5 , Issue.1 , pp. 69-78
  • 17
    • 0004057553 scopus 로고
    • Functional analysis
    • McGraw-Hill, Inc, New York, second edition, MR1157815 92k:46001
    • Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. MR1157815 (92k:46001)
    • (1991) International Series in Pure and Applied Mathematics
    • Rudin, W.1
  • 19
    • 15044349211 scopus 로고    scopus 로고
    • Qian shun Chang and Wei wei Sun. On convergence of multigrid method for nonnegative definite systems. J. Comput. Math., 23(2):177-184, 2005. MR2118053 (2005i:65207)
    • Qian shun Chang and Wei wei Sun. On convergence of multigrid method for nonnegative definite systems. J. Comput. Math., 23(2):177-184, 2005. MR2118053 (2005i:65207)
  • 20
    • 0033639850 scopus 로고    scopus 로고
    • The design and analysis of the generalized finite element method
    • 181(l-3):43-69, MR1734667 2000h:74077
    • T. Strouboulis, I. Babuška, and K. Copps. The design and analysis of the generalized finite element method. Comput. Methods Appl. Mech. Engrg., 181(l-3):43-69, 2000. MR1734667 (2000h:74077)
    • (2000) Comput. Methods Appl. Mech. Engrg
    • Strouboulis, T.1    Babuška, I.2    Copps, K.3
  • 21
    • 0035843805 scopus 로고    scopus 로고
    • The generalized finite element method
    • MR1832655 2002h:65195
    • T. Strouboulis, K. Copps, and I. Babuška. The generalized finite element method. Comput. Methods Appl. Mech. Engrg., 190(32-33):4081-4193, 2001. MR1832655 (2002h:65195)
    • (2001) Comput. Methods Appl. Mech. Engrg , vol.190 , Issue.32-33 , pp. 4081-4193
    • Strouboulis, T.1    Copps, K.2    Babuška, I.3
  • 22
    • 28444494396 scopus 로고    scopus 로고
    • A posteriori error estimation for generalized finite element methods
    • MR2195292 2006i:65180
    • Theofanis Strouboulis, Lin Zhang, Delin Wang, and Ivo Babuška. A posteriori error estimation for generalized finite element methods. Comput. Methods Appl. Mech. Engrg., 195(912):852-879, 2006. MR2195292 (2006i:65180)
    • (2006) Comput. Methods Appl. Mech. Engrg , vol.195 , Issue.912 , pp. 852-879
    • Strouboulis, T.1    Zhang, L.2    Wang, D.3    Babuška, I.4
  • 23
    • 33745298485 scopus 로고    scopus 로고
    • Domain decomposition methods-algorithms and theory
    • of, Springer-Verlag, Berlin, MR2104179 2005g:65006
    • Andrea Toselli and Olof Widlund. Domain decomposition methods-algorithms and theory, volume 34 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 2005. MR2104179 (2005g:65006)
    • (2005) Springer Series in Computational Mathematics , vol.34
    • Toselli, A.1    Widlund, O.2
  • 25
    • 0036016141 scopus 로고    scopus 로고
    • The method of subspace corrections and the method of alternating projections in Hubert space
    • MR1896233 2003f:65095
    • J. Xu and L. Zikatanov. The method of subspace corrections and the method of alternating projections in Hubert space. J. Amer. Math. Soc., 15(3):573-597, 2002. MR1896233 (2003f:65095)
    • (2002) J. Amer. Math. Soc , vol.15 , Issue.3 , pp. 573-597
    • Xu, J.1    Zikatanov, L.2
  • 26
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • MR1193013 93k:65029
    • Jinchao Xu. Iterative methods by space decomposition and subspace correction. SIAM Review, 34:581-613, 1992. MR1193013 (93k:65029)
    • (1992) SIAM Review , vol.34 , pp. 581-613
    • Jinchao, X.1
  • 27
    • 42349098090 scopus 로고    scopus 로고
    • Jinchao Xu and Ludmil T. Zikatanov. On multigrid methods for generalized finite element methods. In Meshfree methods for partial differential equations (Bonn, 2001), 26 of Lect. Notes Comput. Sci. Eng., pages 401-418. Springer, Berlin, 2003. MR2004013
    • Jinchao Xu and Ludmil T. Zikatanov. On multigrid methods for generalized finite element methods. In Meshfree methods for partial differential equations (Bonn, 2001), volume 26 of Lect. Notes Comput. Sci. Eng., pages 401-418. Springer, Berlin, 2003. MR2004013
  • 28
    • 0038869361 scopus 로고
    • Functional analysis
    • Band, Academic Press, Inc, New York, MR0180824 31:5054
    • Kôsaku Yosida. Functional analysis. Die Grundlehren der Mathematischen Wissenschaften, Band 123. Academic Press, Inc., New York, 1965. MR0180824 (31:5054)
    • (1965) Die Grundlehren der Mathematischen Wissenschaften , vol.123
    • Yosida, K.1
  • 29
    • 84971922635 scopus 로고
    • Old and new convergence proofs for multigrid methods
    • Cambridge Univ. Press, Cambridge, MR1224685 94i:65128
    • Harry Yserentant. Old and new convergence proofs for multigrid methods. In Acta numerica, 1993, Acta Numer., pages 285-326. Cambridge Univ. Press, Cambridge, 1993. MR1224685 (94i:65128)
    • (1993) Acta numerica, 1993, Acta Numer , pp. 285-326
    • Yserentant, H.1


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