메뉴 건너뛰기




Volumn 72, Issue 244, 2003, Pages 1711-1730

V-cycle convergence of some multigrid methods for ill-posed problems

Author keywords

Ill posed problem; Multigrid methods

Indexed keywords


EID: 0141976336     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-03-01533-3     Document Type: Article
Times cited : (20)

References (32)
  • 1
    • 0000671861 scopus 로고
    • A new convergence proof for the multigrid method including the V-cycle
    • MR 85h:65233
    • D. Braess, W. Hackbusch, A new convergence proof for the multigrid method including the V-cycle, SIAM J. Numer. Anal. 20 (1983), 967-975. MR 85h:65233
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 967-975
    • Braess, D.1    Hackbusch, W.2
  • 2
    • 0003320310 scopus 로고
    • Multigrid methods
    • Longman Scientific & Technical, Harlow, UK. MR 95b:65002
    • J.H. Bramble, Multigrid methods, Pitman Research Notes in Mathematics Series 294, Longman Scientific & Technical, Harlow, UK, 1993. MR 95b:65002
    • (1993) Pitman Research Notes in Mathematics Series , vol.294
    • Bramble, J.H.1
  • 3
    • 84968502340 scopus 로고
    • The analysis of multigrid algorithms for pseudo-differential operators of order minus one
    • MR 94m:65184
    • J.H. Bramble, Z. Leyk, J.E. Pasciak, The analysis of multigrid algorithms for pseudo-differential operators of order minus one, Math. Comp. 63 (1994), 461-478. MR 94m:65184
    • (1994) Math. Comp. , vol.63 , pp. 461-478
    • Bramble, J.H.1    Leyk, Z.2    Pasciak, J.E.3
  • 4
    • 84968468806 scopus 로고
    • New estimates for multigrid algorithms including the V-cycle
    • MR 94a:65064
    • J.H. Bramble, J.E. Pasciak, New estimates for multigrid algorithms including the V-cycle, Math. Comp. 60 (1993), 447-471. MR 94a:65064
    • (1993) Math. Comp. , vol.60 , pp. 447-471
    • Bramble, J.H.1    Pasciak, J.E.2
  • 5
    • 0034403952 scopus 로고    scopus 로고
    • Computational scales of Sobolev norms with application to preconditioning
    • MR 2000k:65088
    • J.H. Bramble, J.E. Pasciak, P.S. Vassilevski, Computational scales of Sobolev norms with application to preconditioning, Math. Comp. 69 (2000), 463-480. MR 2000k:65088
    • (2000) Math. Comp. , vol.69 , pp. 463-480
    • Bramble, J.H.1    Pasciak, J.E.2    Vassilevski, P.S.3
  • 6
    • 84966255975 scopus 로고
    • Convergence estimates for multigrid algorithms without regularity assumptions
    • MR 91m:65158
    • J.H. Bramble, J.E. Pasciak, J. Wang, J. Xu, Convergence estimates for multigrid algorithms without regularity assumptions, Math. Comp. 57 (1991), 23-45. MR 91m:65158
    • (1991) Math. Comp. , vol.57 , pp. 23-45
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 7
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • MR 90k:65170
    • J.H. Bramble, J.E. Pasciak, J. Xu, Parallel multilevel preconditioners, Math. Comp. 55 (1990), 1-22. MR 90k:65170
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 8
    • 84966233568 scopus 로고
    • Multilevel adaptive solutions to boundary value problems
    • MR 55:4714
    • A. Brandt, Multilevel adaptive solutions to boundary value problems, Math. Comp. 31 (1977), 333-390. MR 55:4714
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 9
    • 0013013557 scopus 로고
    • On projection methods for solving linear ill-posed problems
    • A. Vogel, ed., Vieweg, Braunschweig. MR 90g:65078
    • H.W. Engl, A. Neubauer, On projection methods for solving linear ill-posed problems, in: A. Vogel, ed., Model Optimization in Exploration Geophysics, Vieweg, Braunschweig, 1987, 73-92. MR 90g:65078
    • (1987) Model Optimization in Exploration Geophysics , pp. 73-92
    • Engl, H.W.1    Neubauer, A.2
  • 12
    • 0013018579 scopus 로고
    • Convergence of a general projection method for an operator equation of the first kind
    • MR 90b:65109
    • C.W. Groetsch, A. Neubauer, Convergence of a general projection method for an operator equation of the first kind, Houston J. Mathem. 14 (1988), 201-207. MR 90b:65109
    • (1988) Houston J. Mathem. , vol.14 , pp. 201-207
    • Groetsch, C.W.1    Neubauer, A.2
  • 15
    • 0033406590 scopus 로고    scopus 로고
    • Two-level preconditioners for regularized inverse problems I: Theory
    • MR 2001h:65069
    • M. Hanke, C.R. Vogel, Two-level preconditioners for regularized inverse problems I: Theory, Numer. Math. 83 (1999), 385-402. MR 2001h:65069
    • (1999) Numer. Math. , vol.83 , pp. 385-402
    • Hanke, M.1    Vogel, C.R.2
  • 16
    • 0012966823 scopus 로고    scopus 로고
    • A projection-regularized Newton method for nonlinear ill-posed problems with application to parameter identification problems with finite element discretization
    • MR 2001f:65070
    • B. Kaltenbacher, A projection-regularized Newton method for nonlinear ill-posed problems with application to parameter identification problems with finite element discretization, SIAM J.Numer.Anal. 37 (2000), 1885-1908. MR 2001f:65070
    • (2000) SIAM J.Numer.Anal. , vol.37 , pp. 1885-1908
    • Kaltenbacher, B.1
  • 17
    • 0041734177 scopus 로고    scopus 로고
    • Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems
    • MR 2001h:65070
    • B. Kaltenbacher, Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems, Inverse Problems 16 (2000), 1523-1539. MR 2001h:65070
    • (2000) Inverse Problems , vol.16 , pp. 1523-1539
    • Kaltenbacher, B.1
  • 18
    • 0035419872 scopus 로고    scopus 로고
    • On the regularizing properties of a full multigrid method for ill-posed problems
    • MR 2002h:65094
    • B. Kaltenbacher, On the regularizing properties of a full multigrid method for ill-posed problems, Inverse Problems 17 (2001), 767-788. MR 2002h:65094
    • (2001) Inverse Problems , vol.17 , pp. 767-788
    • Kaltenbacher, B.1
  • 19
    • 0141952784 scopus 로고    scopus 로고
    • V-cycle convergence of some multigrid methods for ill-posed problems
    • University of Linz
    • B. Kaltenbacher, V-cycle convergence of some multigrid methods for ill-posed problems, SFB013-report, University of Linz, 2000.
    • (2000) SFB013-Report
    • Kaltenbacher, B.1
  • 20
    • 0141918357 scopus 로고    scopus 로고
    • Identification of nonlinear B - H curves based on magnetic field computations and using multigrid preconditioners for ill-posed problems
    • B. Kaltenbacher, M. Kaltenbacher, S. Reitzinger, Identification of nonlinear B - H curves based on magnetic field computations and using multigrid preconditioners for ill-posed problems, to appear in Europ. J. Appl. Math., 2002.
    • (2002) Europ. J. Appl. Math.
    • Kaltenbacher, B.1    Kaltenbacher, M.2    Reitzinger, S.3
  • 21
    • 85047694762 scopus 로고    scopus 로고
    • A multigrid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems
    • DOI 10.1007/s002110100375, January
    • B. Kaltenbacher, J. Schicho, A multigrid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems, Numer. Math., DOI 10.1007/s002110100375, January 2002.
    • (2002) Numer. Math.
    • Kaltenbacher, B.1    Schicho, J.2
  • 22
    • 0001224287 scopus 로고
    • Multilevel algorithms for ill-posed problems
    • MR 92k:65090
    • J.T. King, Multilevel algorithms for ill-posed problems, Numer. Math. 61 (1992), 311-334. MR 92k:65090
    • (1992) Numer. Math. , vol.61 , pp. 311-334
    • King, J.T.1
  • 25
    • 0000363718 scopus 로고
    • Regularisierung schecht gestellter Probleme durch Projektionsverfahren
    • MR 58:8238
    • F. Natterer, Regularisierung schecht gestellter Probleme durch Projektionsverfahren, Numer. Math. 28 (1977), 329-341. MR 58:8238
    • (1977) Numer. Math. , vol.28 , pp. 329-341
    • Natterer, F.1
  • 28
    • 0013235011 scopus 로고    scopus 로고
    • On the characterization of self-regularization properties of a fully discrete projection method for Symm's integral equation
    • MR 2001j:65198
    • S.V. Pereverzev, S. Prössdorf, On the characterization of self-regularization properties of a fully discrete projection method for Symm's integral equation, J. Integral Equations Appl. 12 (2000), no. 2, 113-130. MR 2001j:65198
    • (2000) J. Integral Equations Appl. , vol.12 , Issue.2 , pp. 113-130
    • Pereverzev, S.V.1    Prössdorf, S.2
  • 29
    • 0031542819 scopus 로고    scopus 로고
    • A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization
    • MR 97k:65299
    • A. Rieder, A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization, Numer. Math. 75 (1997), 501-522. MR 97k:65299
    • (1997) Numer. Math. , vol.75 , pp. 501-522
    • Rieder, A.1
  • 31
    • 0013286501 scopus 로고
    • Projection methods and self-regularization in ill-posed problems
    • MR 87m:65096
    • G.M. Vainikko, U. Hämarik, Projection methods and self-regularization in ill-posed problems, Sov. Math. 29 (1985), 1-20. MR 87m:65096
    • (1985) Sov. Math. , vol.29 , pp. 1-20
    • Vainikko, G.M.1    Hämarik, U.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.