메뉴 건너뛰기




Volumn 75, Issue 256, 2006, Pages 1913-1929

Regularization of some linear ill-posed problems with discretized random noisy data

Author keywords

General source condition; Operator monotone function; Statistical ill posed problem

Indexed keywords


EID: 33744515791     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-06-01873-4     Document Type: Article
Times cited : (79)

References (17)
  • 1
    • 0004151496 scopus 로고    scopus 로고
    • Springer-Verlag, New York. MR1477662 (98i:15003)
    • Rajendra Bhatia. Matrix analysis. Springer-Verlag, New York, 1997. MR1477662 (98i:15003)
    • (1997) Matrix Analysis
    • Bhatia, R.1
  • 2
    • 0034561754 scopus 로고    scopus 로고
    • Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations
    • MR1790080 (2001h:62055)
    • Alexander Goldenshluger and Sergei V. Pereverzev. Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations. Probab. Theory Related Fields, 118(2):169-186, 2000. MR1790080 (2001h:62055)
    • (2000) Probab. Theory Related Fields , vol.118 , Issue.2 , pp. 169-186
    • Goldenshluger, A.1    Pereverzev, S.V.2
  • 3
    • 0000554469 scopus 로고
    • Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization
    • MR1378036 (97a:65060)
    • Markus Hegland. Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization. Appl. Anal., 59(1-4):207-223, 1995. MR1378036 (97a:65060)
    • (1995) Appl. Anal. , vol.59 , Issue.1-4 , pp. 207-223
    • Hegland, M.1
  • 4
    • 0003771756 scopus 로고
    • Springer-Verlag, Berlin. Isoperimetry and processes. MR1102015 (93c:60001)
    • Michel Ledoux and Michel Talagrand. Probability in Banach spaces. Springer-Verlag, Berlin, 1991. Isoperimetry and processes. MR1102015 (93c:60001)
    • (1991) Probability in Banach Spaces
    • Ledoux, M.1    Talagrand, M.2
  • 5
    • 0000012624 scopus 로고
    • A problem of adaptive estimation in Gaussian white noise
    • MR1091202 (93j:62212)
    • O. V. Lepskiǐ. A problem of adaptive estimation in Gaussian white noise. Tear. Veroyatnost. i Primenen., 35(3):459-470, 1990. MR1091202 (93j:62212)
    • (1990) Tear. Veroyatnost. i Primenen. , vol.35 , Issue.3 , pp. 459-470
    • Lepskiǐ, O.V.1
  • 6
    • 0030269038 scopus 로고    scopus 로고
    • Statistical inverse estimation in Hilbert scales
    • MR1409127 (97k:62095)
    • Bernard A. Mair and Frits H. Ruymgaart. Statistical inverse estimation in Hilbert scales. SIAM J. Appl. Math., 56(5): 1424-1444, 1996. MR1409127 (97k:62095)
    • (1996) SIAM J. Appl. Math. , vol.56 , Issue.5 , pp. 1424-1444
    • Mair, B.A.1    Ruymgaart, F.H.2
  • 7
    • 0034580744 scopus 로고    scopus 로고
    • Optimal discretization of inverse problems in Hilbert scales. Regularization and self-regularization of projection methods
    • MR1856240 (2002g:62063)
    • Peter Mathé and Sergei V. Pereverzev. Optimal discretization of inverse problems in Hilbert scales. Regularization and self-regularization of projection methods. SIAM J. Numer. Anal., 38(6):1999-2021, 2001. MR1856240 (2002g:62063)
    • (2001) SIAM J. Numer. Anal. , vol.38 , Issue.6 , pp. 1999-2021
    • Mathé, P.1    Pereverzev, S.V.2
  • 8
    • 0036697653 scopus 로고    scopus 로고
    • Moduli of continuity for operator valued functions
    • MR1923828 (2003g:47029)
    • Peter Mathé and Sergei V. Pereverzev. Moduli of continuity for operator valued functions. Numer. Funct. Anal. Optim., 23(5-6):623-631, 2002. MR1923828 (2003g:47029)
    • (2002) Numer. Funct. Anal. Optim. , vol.23 , Issue.5-6 , pp. 623-631
    • Mathé, P.1    Pereverzev, S.V.2
  • 9
    • 0346946904 scopus 로고    scopus 로고
    • Discretization strategy for linear ill-posed problems in variable Hilbert scales
    • MR2036530 (2004k:65097)
    • Peter Mathé and Sergei V. Pereverzev. Discretization strategy for linear ill-posed problems in variable Hilbert scales. Inverse Problems, 19(6):1263-1277, 2003. MR2036530 (2004k:65097)
    • (2003) Inverse Problems , vol.19 , Issue.6 , pp. 1263-1277
    • Mathé, P.1    Pereverzev, S.V.2
  • 10
    • 0038339461 scopus 로고    scopus 로고
    • Geometry of linear ill-posed problems in variable Hilbert scales
    • MR1984890 (2004i:47021)
    • Peter Mathé and Sergei V. Pereverzev. Geometry of linear ill-posed problems in variable Hilbert scales. Inverse Problems, 19(3):789-803, 2003. MR1984890 (2004i:47021)
    • (2003) Inverse Problems , vol.19 , Issue.3 , pp. 789-803
    • Mathé, P.1    Pereverzev, S.V.2
  • 11
    • 0037227075 scopus 로고    scopus 로고
    • Morozov's discrepancy principle under general source conditions
    • MR1962084 (2004a:65069)
    • M. T. Nair, E. Schock, and U. Tautenhahn. Morozov's discrepancy principle under general source conditions. Z. Anal. Anwendungen, 22(1):199-214, 2003. MR1962084 (2004a:65069)
    • (2003) Z. Anal. Anwendungen , vol.22 , Issue.1 , pp. 199-214
    • Nair, M.T.1    Schock, E.2    Tautenhahn, U.3
  • 12
    • 33750885690 scopus 로고
    • Eigenvalues and s-Numbers. Geest & Portig, Leipzig. MR0917067 (88j:47022a)
    • A. Pietsch. Eigenvalues and s-Numbers, volume 43 of Math. und ihre Anw. in Phys. und Technik. Geest & Portig, Leipzig, 1987. MR0917067 (88j:47022a)
    • (1987) Math. und Ihre Anw. in Phys. und Technik , vol.43
    • Pietsch, A.1
  • 13
    • 0000056063 scopus 로고
    • Optimal filtration of square-integrable signals in Gaussian noise
    • MR0624591 (82j:93048)
    • M. S. Pinsker. Optimal filtration of square-integrable signals in Gaussian noise. Problems Inform. Transmission, 16(2):52-68, 1980. MR0624591 (82j:93048)
    • (1980) Problems Inform. Transmission , vol.16 , Issue.2 , pp. 52-68
    • Pinsker, M.S.1
  • 14
    • 0000414254 scopus 로고    scopus 로고
    • Error estimates for regularization methods in Hilbert scales
    • MR1427456 (97k:65148)
    • Ulrich Tautenhahn. Error estimates for regularization methods in Hilbert scales. SIAM J. Numer. Anal, 33(6):2120-2130, 1996. MR1427456 (97k:65148)
    • (1996) SIAM J. Numer. Anal , vol.33 , Issue.6 , pp. 2120-2130
    • Tautenhahn, U.1
  • 15
    • 0034179341 scopus 로고    scopus 로고
    • On the best rate of adaptive estimation in some inverse problems
    • MR1769957 (2001c:62058)
    • Alexandre Tsybakov. On the best rate of adaptive estimation in some inverse problems. C. R. Acad. Sci. Paris Sér. I Math., 330(9):835-840, 2000. MR1769957 (2001c:62058)
    • (2000) C. R. Acad. Sci. Paris Sér. i Math. , vol.330 , Issue.9 , pp. 835-840
    • Tsybakov, A.1
  • 17
    • 0013110835 scopus 로고    scopus 로고
    • Computational methods for inverse problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. MR1928831 (2003i:65004)
    • Curtis R. Vogel. Computational methods for inverse problems, volume 23 of Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002. MR1928831 (2003i:65004)
    • (2002) Frontiers in Applied Mathematics , vol.23
    • Vogel, C.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.