메뉴 건너뛰기




Volumn 15, Issue 1, 2007, Pages 83-98

On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in L2

Author keywords

Approximate source condition; Distance function; Eigenvalue problem; Integral operator; Linear ill posed problem; Regularization

Indexed keywords


EID: 34248360411     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/JIIP.2007.004     Document Type: Article
Times cited : (6)

References (26)
  • 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
  • 6
    • 21244472723 scopus 로고    scopus 로고
    • Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems
    • DOI 10.1163/1569394053978524
    • M. Freitag and B. Hofmann, Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems. J. Inv. Ill-Posed Problems 13 (2005), 123-148. (Pubitemid 40898522)
    • (2005) Journal of Inverse and Ill-Posed Problems , vol.13 , Issue.2 , pp. 123-148
    • Freitag, M.1    Hofmann, B.2
  • 7
    • 0000554469 scopus 로고
    • Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization
    • M. Hegland, Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization. Appl. Anal. 59 (1995), 207-223.
    • (1995) Appl. Anal. , vol.59 , pp. 207-223
    • Hegland, M.1
  • 8
    • 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 (2006), 351-371. (Pubitemid 43106076)
    • (2006) Mathematical Methods in the Applied Sciences , vol.29 , Issue.3 , pp. 351-371
    • Hofmann, B.1
  • 9
    • 37549043916 scopus 로고    scopus 로고
    • Approximate source conditions in regularization - New analytical results and numerical studies
    • B. Hofmann, D. Düvelmeyer, and K. Krumbiegel, Approximate source conditions in regularization - new analytical results and numerical studies. Journal Mathematical Modelling and Analysis 11 (2006), 41-56.
    • (2006) Journal Mathematical Modelling and Analysis , vol.11 , pp. 41-56
    • Hofmann, B.1    Düvelmeyer, D.2    Krumbiegel, K.3
  • 12
    • 21944452909 scopus 로고    scopus 로고
    • On ill-posedness measures and space change in Sobolev scales
    • B. Hofmann and U. Tautenhahn, On ill-posedness measures and space change in Sobolev scales. Zeitschrif f. Analysis und Anw. 16 (1997), 979-1000.
    • (1997) Zeitschrif f. Analysis und Anw. , vol.16 , pp. 979-1000
    • Hofmann, B.1    Tautenhahn, U.2
  • 13
    • 17444395614 scopus 로고    scopus 로고
    • Some results and a conjecture on the degree of ill-posedness for integration operators with weights
    • DOI 10.1088/0266-5611/21/2/001
    • B. Hofmann and L. von Wolfersdorf, Some results and a conjecture on the degree of ill-posedness for integration operators with weights. Inverse Problems 21 (2005), 427-433. (Pubitemid 40540973)
    • (2005) Inverse Problems , vol.21 , Issue.2 , pp. 427-433
    • Hofmann, B.1    Von Wolfersdorf, L.2
  • 14
    • 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 (2005), 805-820. (Pubitemid 40666655)
    • (2005) Inverse Problems , vol.21 , Issue.3 , pp. 805-820
    • Hofmann, B.1    Yamamoto, M.2
  • 15
    • 0034187252 scopus 로고    scopus 로고
    • Regularization of exponentially ill-posed problems
    • T. Hohage, Regularization of exponentially ill-posed problems. Numer. Funct. Anal. & Optimiz. 21 (2000), 439-464.
    • (2000) Numer. Funct. Anal. & Optimiz. , vol.21 , pp. 439-464
    • Hohage, T.1
  • 16
    • 21244441586 scopus 로고    scopus 로고
    • Saturation of regularization methods for linear ill-posed problems in hilbert spaces
    • DOI 10.1137/S0036142903420947
    • P. Mathé, Saturation of regularization methods for linear ill-posed problems in Hilbert spaces. SIAM J. Numer. Anal. 42 (2004), 968-973. (Pubitemid 40892104)
    • (2004) SIAM Journal on Numerical Analysis , vol.42 , Issue.3 , pp. 968-973
    • Mathe, P.1
  • 17
    • 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 (2003), 789-803.
    • (2003) Inverse Problems , vol.19 , pp. 789-803
    • Mathé, P.1    Pereverzev, S.V.2
  • 18
    • 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 (2003), 1263-1277.
    • (2003) Inverse Problems , vol.19 , pp. 1263-1277
    • Mathé, P.1    Pereverzev, S.V.2
  • 19
    • 33744515791 scopus 로고    scopus 로고
    • Regularization of some linear ill-posed problems with discretized random noisy data
    • -, Regularization of some linear ill-posed problems with discretized random noisy data. Mathematics of Computation 75 (2006), 1913-1929.
    • (2006) Mathematics of Computation , vol.75 , pp. 1913-1929
    • Mathé, P.1    Pereverzev, S.V.2
  • 20
    • 33846083183 scopus 로고    scopus 로고
    • Interpolation in variable Hilbert scales with application to inverse problems
    • DOI 10.1088/0266-5611/22/6/022, PII S0266561106281218, 022
    • P. Mathé and U. Tautenhahn, Interpolation in variable Hilbert scales with application to inverse problems. Inverse Problems 22 (2006), 2271-2297. (Pubitemid 46069513)
    • (2006) Inverse Problems , vol.22 , Issue.6 , pp. 2271-2297
    • Mathe, P.1    Tautenhahn, U.2
  • 21
    • 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 (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
  • 22
    • 0043005507 scopus 로고
    • A new approach to classification and regularization of ill-posed operator equations
    • H.W. Engl and C.W. Groetsch (Eds). Acad. Press, Orlando
    • M. Z. Nashed, A new approach to classification and regularization of ill-posed operator equations. In: Inverse and Ill-posed Problems, H.W. Engl and C.W. Groetsch (Eds). Acad. Press, Orlando, 1987, 53-75.
    • (1987) Inverse and Ill-posed Problems , pp. 53-75
    • Nashed, M.Z.1
  • 23
    • 21244484291 scopus 로고
    • On converse and saturation results for regularization methods
    • E. Schock (Ed). Shaker, Aachen
    • A. Neubauer, On converse and saturation results for regularization methods. In: Beiträge zur angewandten Analysis und Informatik, E. Schock (Ed). Shaker, Aachen, 1994, 262-270.
    • (1994) Beiträge Zur Angewandten Analysis und Informatik , pp. 262-270
    • Neubauer, A.1
  • 24
    • 0032047113 scopus 로고    scopus 로고
    • Optimality for ill-posed problems under general source conditions
    • U. Tautenhahn, Optimality for ill-posed problems under general source conditions. Numer. Funct. Anal. & Optimiz. 19 (1998), 377-398. (Pubitemid 128508292)
    • (1998) Numerical Functional Analysis and Optimization , vol.19 , Issue.3-4 , pp. 377-398
    • Tautenhahn, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.