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Volumn 15, Issue 4, 2007, Pages 419-439

On the quasioptimal regularization parameter choices for solving ill-posed problems

Author keywords

Discrepancy principle; Ill posed problems; Lepskii principle; Monotone error rule; Quasioptimal choice; Regularization parameter

Indexed keywords


EID: 34547683559     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/JIIP.2007.023     Document Type: Article
Times cited : (28)

References (30)
  • 1
    • 28544447290 scopus 로고    scopus 로고
    • A Lepskij-type stopping rule for regularized Newton methods
    • DOI 10.1088/0266-5611/21/6/011, PII S0266561105022355
    • F. Bauer and T. Hohage, A Lepskij-type stopping rule for regularized Newton methods. Inverse Problems 21, 6 (2005), 1975-1991. (Pubitemid 41744510)
    • (2005) Inverse Problems , vol.21 , Issue.6 , pp. 1975-1991
    • Bauer, F.1    Hohage, T.2
  • 2
    • 28544447018 scopus 로고    scopus 로고
    • Regularization without preliminary knowledge of smoothness and error behaviour
    • DOI 10.1017/S0956792505006236, PII S0956792505006236
    • F. Bauer and S. Pereverzev, Regularization without preliminary knowledge of smoothness and error behaviour. European J. Appl. Math. 16, 3 (2005), 303-317. (Pubitemid 41742826)
    • (2005) European Journal of Applied Mathematics , vol.16 , Issue.3 , pp. 303-317
    • Bauer, F.1    Pereverzev, S.2
  • 3
    • 85064780549 scopus 로고    scopus 로고
    • Convergence rates for Tikhonov regularization from different kinds of smoothness conditions
    • A. Böttcher, B. Hofmann, U. Tautenhahn, and M. Yamamoto, Convergence rates for Tikhonov regularization from different kinds of smoothness conditions. Applicable Analysis 85 (2006), 555-578.
    • (2006) Applicable Analysis , vol.85 , pp. 555-578
    • Böttcher, A.1    Hofmann, B.2    Tautenhahn, U.3    Yamamoto, M.4
  • 4
    • 84966214028 scopus 로고
    • An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates
    • H. Gfrerer, An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates. Math. Comp. 49, 180 (1987), 507-522.
    • (1987) Math. Comp. , vol.49 , Issue.180 , pp. 507-522
    • Gfrerer, H.1
  • 5
    • 5844423089 scopus 로고    scopus 로고
    • On the a posteriori parameter choice in regularization methods
    • U. Hämarik and T. Raus, On the a posteriori parameter choice in regularization methods. Proc. Estonian Acad. Sci. Phys. Math. 48, 2 (1999), 133-145.
    • (1999) Proc. Estonian Acad. Sci. Phys. Math. , vol.48 , Issue.2 , pp. 133-145
    • Hämarik, U.1    Raus, T.2
  • 7
    • 33745766913 scopus 로고    scopus 로고
    • On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data
    • -, On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data. J. Inv. Ill-Posed Problems 14, 3 (2006), 251-266.
    • (2006) J. Inv. Ill-Posed Problems , vol.14 , Issue.3 , pp. 251-266
    • Hämarik, U.1    Raus, T.2
  • 8
    • 21944442815 scopus 로고    scopus 로고
    • On the monotone error rule for parameter choice in iterative and continuous regularization methods
    • U. Hämarik and U. Tautenhahn, On the monotone error rule for parameter choice in iterative and continuous regularization methods. BIT 41, 5 (2001), 1029-1038.
    • (2001) BIT , vol.41 , Issue.5 , pp. 1029-1038
    • Hämarik, U.1    Tautenhahn, U.2
  • 9
    • 30844472201 scopus 로고    scopus 로고
    • Approximate source conditions in Tikhonov-Phillips regularization and consequences for inverse problems with multiplication operators
    • DOI 10.1002/mma.686
    • B. Hofmann, Approximate source conditions in Tikhonov-Phillips regularization and consequences for inverse problems with multiplication operators. Mathematical Methods in the Applied Sciences 29, 3 (2006), 351-371. (Pubitemid 43106076)
    • (2006) Mathematical Methods in the Applied Sciences , vol.29 , Issue.3 , pp. 351-371
    • Hofmann, B.1
  • 10
    • 18744408756 scopus 로고    scopus 로고
    • Convergence rates for Tikhonov regularization based on range inclusions
    • DOI 10.1088/0266-5611/21/3/002, PII S0266561105920017
    • B. Hofmann and M. Yamamoto, Convergence rates for Tikhonov regularization based on range inclusions. Inverse Problems 21, 3 (2005), 805-820. (Pubitemid 40666655)
    • (2005) Inverse Problems , vol.21 , Issue.3 , pp. 805-820
    • Hofmann, B.1    Yamamoto, M.2
  • 11
    • 0034187252 scopus 로고    scopus 로고
    • Regularization of exponentially ill-posed problems
    • T. Hohage, Regularization of exponentially ill-posed problems. Numerical Functional Analysis and Optimization 21, 3 (2000), 439-464.
    • (2000) Numerical Functional Analysis and Optimization , vol.21 , Issue.3 , pp. 439-464
    • Hohage, T.1
  • 12
    • 0038339461 scopus 로고    scopus 로고
    • Geometry of linear ill-posed problems in variable Hilbert scales
    • P. Mathé and S. V. Pereverzev, Geometry of linear ill-posed problems in variable Hilbert scales. Inverse Problems 19, 3 (2003), 789-803.
    • (2003) Inverse Problems , vol.19 , Issue.3 , pp. 789-803
    • Mathé, P.1    Pereverzev, S.V.2
  • 13
    • 0346946904 scopus 로고    scopus 로고
    • Discretization strategy for linear ill-posed problems in variable Hilbert scales
    • -, Discretization strategy for linear ill-posed problems in variable Hilbert scales. Inverse Problems 19, 6 (2003), 1263-1277.
    • (2003) Inverse Problems , vol.19 , Issue.6 , pp. 1263-1277
    • Mathé, P.1    Pereverzev, S.V.2
  • 14
    • 33646823795 scopus 로고    scopus 로고
    • The discretized discrepancy principle under general source conditions
    • -, The discretized discrepancy principle under general source conditions. Journal of Complexity 22, 3 (2006), 371-381.
    • (2006) Journal of Complexity , vol.22 , Issue.3 , pp. 371-381
    • Mathé, P.1    Pereverzev, S.V.2
  • 15
    • 0000739264 scopus 로고
    • On the solution of functional equations by the method of regularization
    • V. A. Morozov, On the solution of functional equations by the method of regularization. Soviet Math. Dokl. 7 (1966), 414-417.
    • (1966) Soviet Math. Dokl. , vol.7 , pp. 414-417
    • Morozov, V.A.1
  • 16
    • 28544453228 scopus 로고    scopus 로고
    • Regularization in Hilbert scales under general smoothing conditions
    • DOI 10.1088/0266-5611/21/6/003, PII S0266561105030686
    • M. T. Nair, S. V. Pereverzev, and U. Tautenhahn, Regularization in Hilbert scales under general smoothing conditions. Inverse Problems 21, 6 (2005), 1851-1869. (Pubitemid 41744502)
    • (2005) Inverse Problems , vol.21 , Issue.6 , pp. 1851-1869
    • Nair, M.T.1    Pereverzev, S.V.2    Tautenhahn, U.3
  • 17
    • 0037227075 scopus 로고    scopus 로고
    • Morozov's discrepancy principle under general source conditions
    • M. T. Nair, E. Schock, and U. Tautenhahn, Morozov's discrepancy principle under general source conditions. Z. Anal. Anwendungen 22, 1 (2003), 199-214.
    • (2003) Z. Anal. Anwendungen , vol.22 , Issue.1 , pp. 199-214
    • Nair, M.T.1    Schock, E.2    Tautenhahn, U.3
  • 18
    • 3042543149 scopus 로고    scopus 로고
    • Lavrentiev regularization for linear ill-posed problems under general source conditions
    • M. T. Nair and U. Tautenhahn, Lavrentiev regularization for linear ill-posed problems under general source conditions. Z. Anal. Anwendungen 23, 1 (2004), 167-185.
    • (2004) Z. Anal. Anwendungen , vol.23 , Issue.1 , pp. 167-185
    • Nair, M.T.1    Tautenhahn, U.2
  • 19
    • 33750173498 scopus 로고    scopus 로고
    • On the adaptive selection of the parameter in regularization of ill-posed problems
    • DOI 10.1137/S0036142903433819
    • S. V. Pereverzev and E. Schock, On the adaptive selection of the parameter in the regularization of ill-posed problems. SIAM J. Numerical Analysis 43 (2005), 2060-2076. (Pubitemid 44598672)
    • (2005) SIAM Journal on Numerical Analysis , vol.43 , Issue.5 , pp. 2060-2076
    • Pereverzev, S.1    Schock, E.2
  • 20
    • 0008325004 scopus 로고
    • Residue principle for ill-posed problems
    • in Russian
    • T. Raus, Residue principle for ill-posed problems. Acta et Comment. Univ. Tartuensis 672 (1984), 16-26 (in Russian).
    • (1984) Acta et Comment. Univ. Tartuensis , vol.672 , pp. 16-26
    • Raus, T.1
  • 21
    • 0002729317 scopus 로고
    • On the discrepancy principle for solution of ill-posed problems with non-selfadjoint operators
    • in Russian
    • -, On the discrepancy principle for solution of ill-posed problems with non-selfadjoint operators. Acta et Comment. Univ. Tartuensis 715 (1985), 12-20 (in Russian).
    • (1985) Acta et Comment. Univ. Tartuensis , vol.715 , pp. 12-20
    • Raus, T.1
  • 22
    • 21944436340 scopus 로고
    • An a posteriori choice of the regularization parameter in case of approximately given error bound of data
    • -, An a posteriori choice of the regularization parameter in case of approximately given error bound of data. Acta et comment. Univ. Tartuensis 913 (1990), 73-87.
    • (1990) Acta et Comment. Univ. Tartuensis , vol.913 , pp. 73-87
    • Raus, T.1
  • 23
    • 5844390290 scopus 로고
    • About regularization parameter choice in case of approximately given error bounds of data
    • -, About regularization parameter choice in case of approximately given error bounds of data. Acta et comment. Univ. Tartuensis 937 (1992), 77-89.
    • (1992) Acta et Comment. Univ. Tartuensis , vol.937 , pp. 77-89
    • Raus, T.1
  • 24
    • 5844417652 scopus 로고
    • On the regularization parameter choice for ill-posed problems with a quasisolution
    • VSP, Utrecht / TVP, Moscow
    • -, On the regularization parameter choice for ill-posed problems with a quasisolution. In: Ill-Posed Problems in Natural Science. VSP, Utrecht / TVP, Moscow, 1992, 144-152.
    • (1992) Ill-Posed Problems in Natural Science , pp. 144-152
    • Raus, T.1
  • 25
    • 72749120451 scopus 로고    scopus 로고
    • On the a posteriori parameter choice for the determination of a quasisolution
    • Estonian Mathematical Society, Tartu
    • -, On the a posteriori parameter choice for the determination of a quasisolution. In: Differential and Integral Equations: Theory and Numerical Analysis. Estonian Mathematical Society, Tartu, 1999, 81-96.
    • (1999) Differential and Integral Equations: Theory and Numerical Analysis , pp. 81-96
    • Raus, T.1
  • 27
    • 0032047113 scopus 로고    scopus 로고
    • Optimality for ill-posed problems under general source conditions
    • -, Optimality for ill-posed problems under general source conditions. Numer. Funct. Anal. Optim. 19, 3/4 (1998), 377-398.
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , Issue.3-4 , pp. 377-398
    • Tautenhahn, U.1
  • 28
    • 77956266051 scopus 로고    scopus 로고
    • On order optimal regularization under general source conditions
    • -, On order optimal regularization under general source conditions. Proc. Estonian Acad. Sci. Phys. Math. 53, 2 (2004), 116-123.
    • (2004) Proc. Estonian Acad. Sci. Phys. Math. , vol.53 , Issue.2 , pp. 116-123
    • Tautenhahn, U.1
  • 29
    • 0013298158 scopus 로고    scopus 로고
    • The use of monotonicity for choosing the regularization parameter in ill-posed problems
    • PII S0266561199035406
    • U. Tautenhahn and U. Hämarik, The use of monotonicity for choosing the regularization parameter in ill-posed problems. Inverse Problems 15, 6 (1999), 1487-1505. (Pubitemid 129655864)
    • (1999) Inverse Problems , vol.15 , Issue.6 , pp. 1487-1505
    • Tautenhahn, U.1    Hamarik, U.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.