메뉴 건너뛰기




Volumn 22, Issue 1, 2006, Pages 155-174

A multilevel augmentation method for solving ill-posed operator equations

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; MATHEMATICAL OPERATORS; NUMERICAL ANALYSIS;

EID: 31844438376     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/22/1/009     Document Type: Article
Times cited : (54)

References (32)
  • 2
    • 21744452540 scopus 로고    scopus 로고
    • The Petrov-Galerkin methods for second kind integral equations: II. Multiwavelet scheme
    • Chen Z, Micchelli C A and Xu Y 1997 The Petrov-Galerkin methods for second kind integral equations: II. Multiwavelet scheme Adv. Comput. Math. 7 199-233
    • (1997) Adv. Comput. Math. , vol.7 , pp. 199-233
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 3
    • 0033456757 scopus 로고    scopus 로고
    • A construction of interpolating wavelets on invariant sets
    • Chen Z. Micchelli C A and Xu Y 1999 A construction of interpolating wavelets on invariant sets Math. Comput. 68 1560-87
    • (1999) Math. Comput. , vol.68 , pp. 1560-1587
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 4
    • 0035888656 scopus 로고    scopus 로고
    • A multilevel method for solving operator equations
    • Chen Z, Micchelli C A and Xu Y 2001 A multilevel method for solving operator equations J. Math. Anal. Appl. 262 688-99
    • (2001) J. Math. Anal. Appl. , vol.262 , pp. 688-699
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 6
    • 0036556665 scopus 로고    scopus 로고
    • Fast collocation methods for second kind integral equations
    • Chen Z, Micchelli C A and Xu Y 2002 Fast collocation methods for second kind integral equations SIAM J. Numer. Anal. 40 344-75
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 344-375
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 7
    • 31844437667 scopus 로고    scopus 로고
    • Multilevel augmentation methods for solving operator equations
    • Chen Z, Wu B and Xu Y 2005 Multilevel augmentation methods for solving operator equations Numer. Math. J. Chin. Univ. 1431-55
    • (2005) Numer. Math. J. Chin. Univ. , vol.14 , pp. 31-55
    • Chen, Z.1    Wu, B.2    Xu, Y.3
  • 8
    • 0000827236 scopus 로고
    • Wavelet approximation methods for pseudodifferential equations: II. Matrix compression and fast solutions
    • Dahmen W, Proessdorf S and Schneider R 1993 Wavelet approximation methods for pseudodifferential equations: II. Matrix compression and fast solutions Adv. Comput. Math. 1 259-335
    • (1993) Adv. Comput. Math. , vol.1 , pp. 259-335
    • Dahmen, W.1    Proessdorf, S.2    Schneider, R.3
  • 9
    • 85016849323 scopus 로고    scopus 로고
    • Wavelet-Galerkin methods for ill-posed problems
    • Dicken V and Maass P 1996 Wavelet-Galerkin methods for ill-posed problems J. Inverse Ill-Posed Problems 4 203-21
    • (1996) J. Inverse Ill-posed Problems , vol.4 , pp. 203-221
    • Dicken, V.1    Maass, P.2
  • 11
    • 0033406590 scopus 로고    scopus 로고
    • Two-level preconditioners for regularized inverse problems: I. Theory
    • Hanke M and Vogel C R 1999 Two-level preconditioners for regularized inverse problems: I. Theory Numer. Math. 83 385-402
    • (1999) Numer. Math. , vol.83 , pp. 385-402
    • Hanke, M.1    Vogel, C.R.2
  • 13
    • 5844409017 scopus 로고
    • On the discretization error in regularized projection methods with parameter choice by discrepancy principle
    • ed A N Tikhonov (Utrecht: VSP/Moscow: TVP)
    • Hämarik U 1992 On the discretization error in regularized projection methods with parameter choice by discrepancy principle Ill-Posed Problems in Natural Sciences ed A N Tikhonov (Utrecht: VSP/Moscow: TVP) pp 24-9
    • (1992) Ill-posed Problems in Natural Sciences , pp. 24-29
    • Hämarik, U.1
  • 14
    • 24444468135 scopus 로고
    • Quasioptimal error estimate for the regularized Ritz-Galerkin method with the a posteriori choice of the parameter
    • Hämarik U 1992 Quasioptimal error estimate for the regularized Ritz-Galerkin method with the a posteriori choice of the parameter Acta Comment. Univ. Tartuensis 937 63-76
    • (1992) Acta Comment. Univ. Tartuensis , vol.937 , pp. 63-76
    • Hämarik, U.1
  • 15
    • 0042255147 scopus 로고
    • On the parameter choice in the regularized Ritz-Galerkin method
    • Hämarik U 1993 On the parameter choice in the regularized Ritz-Galerkin method Proc. Estonian Acad. Sci., Phys. Math. 42 133-43
    • (1993) Proc. Estonian Acad. Sci., Phys. Math. , vol.42 , pp. 133-143
    • Hämarik, U.1
  • 16
    • 0041912910 scopus 로고    scopus 로고
    • Self-regularization by projection for noisy pseudodifferential equations of negative order
    • Harbrecht H, Pereverzev S and Schneider R 2003 Self-regularization by projection for noisy pseudodifferential equations of negative order Numer. Math. 95 123-43
    • (2003) Numer. Math. , vol.95 , pp. 123-143
    • Harbrecht, H.1    Pereverzev, S.2    Schneider, R.3
  • 17
    • 0039447792 scopus 로고    scopus 로고
    • On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
    • Jin Q and Hou Z 1999 On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems Numer. Math. 83 139-59
    • (1999) Numer. Math. , vol.83 , pp. 139-159
    • Jin, Q.1    Hou, Z.2
  • 18
    • 0035419872 scopus 로고    scopus 로고
    • On the regularizing properties of a full multigrid method for ill-posed problems
    • Kaltenbacher B 2001 On the regularizing properties of a full multigrid method for ill-posed problems Inverse Problem 17 767-88
    • (2001) Inverse Problem , vol.17 , pp. 767-788
    • Kaltenbacher, B.1
  • 19
    • 0035614688 scopus 로고    scopus 로고
    • An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
    • Maass P, Pereverzev S V, Ramlau R and Solodky S G 2001 An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection Numer. Math. 87 485-502
    • (2001) Numer. Math. , vol.87 , pp. 485-502
    • Maass, P.1    Pereverzev, S.V.2    Ramlau, R.3    Solodky, S.G.4
  • 20
    • 0346946904 scopus 로고    scopus 로고
    • Discretization strategy for linear ill-posed problems in variable Hubert scales
    • Mathé P and Pereverzev S V 2003 Discretization strategy for linear ill-posed problems in variable Hubert scales Inverse Problems 19 1263-77
    • (2003) Inverse Problems , vol.19 , pp. 1263-1277
    • Mathé, P.1    Pereverzev, S.V.2
  • 21
    • 0028499152 scopus 로고
    • Using the matrix refinement equation for the construction of wavelets on invariant sets
    • Micchelli C A and Xu Y 1994 Using the matrix refinement equation for the construction of wavelets on invariant sets Appl. Comput. Harmon. Anal. 1 391-401
    • (1994) Appl. Comput. Harmon. Anal. , vol.1 , pp. 391-401
    • Micchelli, C.A.1    Xu, Y.2
  • 22
    • 0030785892 scopus 로고    scopus 로고
    • Reconstruction and decomposition algorithms for biorthogonal multiwavelets
    • Micchelli C A and Xu Y 1997 Reconstruction and decomposition algorithms for biorthogonal multiwavelets Multidimens. Syst. Signal Process. 8 31-69
    • (1997) Multidimens. Syst. Signal Process. , vol.8 , pp. 31-69
    • Micchelli, C.A.1    Xu, Y.2
  • 23
    • 0031277073 scopus 로고    scopus 로고
    • Wavelet Galerkin methods for second-kind integral equations
    • Micchelli C A, Xu Y and Zhao Y 1997 Wavelet Galerkin methods for second-kind integral equations J. Comput. Appl. Math. 86251-70
    • (1997) J. Comput. Appl. Math. , vol.86 , pp. 251-270
    • Micchelli, C.A.1    Xu, Y.2    Zhao, Y.3
  • 24
    • 0008336402 scopus 로고    scopus 로고
    • The Galerkin scheme for Lavrentiev's m-times iterated method to solve linear accretive Volterra integral equations of the first kind
    • Plato R 1997 The Galerkin scheme for Lavrentiev's m-times iterated method to solve linear accretive Volterra integral equations of the first kind BIT 37 404-23
    • (1997) BIT , vol.37 , pp. 404-423
    • Plato, R.1
  • 25
    • 0030524567 scopus 로고    scopus 로고
    • On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations
    • Plato R 1996 On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations Numer. Math. 75 99-120
    • (1996) Numer. Math. , vol.75 , pp. 99-120
    • Plato, R.1
  • 26
    • 0000710028 scopus 로고    scopus 로고
    • On pseudo-optimal parameter choices and stopping rules for regularization methods in Banach spaces
    • Plato R and Hämarik U 1996 On pseudo-optimal parameter choices and stopping rules for regularization methods in Banach spaces Numer. Funct. Anal. Optim. 17 181-95
    • (1996) Numer. Funct. Anal. Optim. , vol.17 , pp. 181-195
    • Plato, R.1    Hämarik, U.2
  • 27
    • 0003056816 scopus 로고
    • On the regularization of projection methods for solving ill-posed problems
    • Plato R and Vainikko G 1990 On the regularization of projection methods for solving ill-posed problems Numer. Math. 57 63-79
    • (1990) Numer. Math. , vol.57 , pp. 63-79
    • Plato, R.1    Vainikko, G.2
  • 28
    • 0031542819 scopus 로고    scopus 로고
    • A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization
    • Rieder A 1997 A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization Numer. Math. 75 501-22
    • (1997) Numer. Math. , vol.75 , pp. 501-522
    • Rieder, A.1
  • 30
    • 23244451062 scopus 로고    scopus 로고
    • On a quasi-optimal regularized projection method for solving operator equations of the first kind
    • Solodky S G 2005 On a quasi-optimal regularized projection method for solving operator equations of the first kind Inverse Problems 21 1473-85
    • (2005) Inverse Problems , vol.21 , pp. 1473-1485
    • Solodky, S.G.1
  • 31
    • 31844457176 scopus 로고    scopus 로고
    • A posteriori parameter choice strategy for nonlinear monotone operator equations
    • Yang H and Hou Z 2002 A posteriori parameter choice strategy for nonlinear monotone operator equations Acta Math. Appl. Sinica 18 289-94
    • (2002) Acta Math. Appl. Sinica , vol.18 , pp. 289-294
    • Yang, H.1    Hou, Z.2
  • 32
    • 31844433754 scopus 로고    scopus 로고
    • Convergence rates of regularized solutions and parameter choice strategy for positive semi-definite operator equation
    • Chinese edition
    • Yang H and Hou Z 1998 Convergence rates of regularized solutions and parameter choice strategy for positive semi-definite operator equation Numer. Math. J. Chin. Univ. 20 245-51 (Chinese edition)
    • (1998) Numer. Math. J. Chin. Univ. , vol.20 , pp. 245-251
    • Yang, H.1    Hou, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.