메뉴 건너뛰기




Volumn 18, Issue 1, 1999, Pages 37-46

On Morozov's method for tikhonov regularization as an optimal order yielding algorithm

Author keywords

Hilbert scales; Ill posed equations; Interpolation inequalities; Order optimal algorithms; Tikhonov regularization

Indexed keywords


EID: 22644452310     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/868     Document Type: Article
Times cited : (14)

References (14)
  • 1
    • 0001840812 scopus 로고
    • Regularization methods for the stable solution of inverse problems
    • Engl, H. W.: Regularization methods for the stable solution of inverse problems. Surveys Math. Indust. 3 (1993), 71 - 143.
    • (1993) Surveys Math. Indust. , vol.3 , pp. 71-143
    • Engl, H.W.1
  • 5
    • 0018999755 scopus 로고
    • Regularization with differential operators
    • Locker, J. and P. M. Prenter: Regularization with differential operators. J. Math. Anal. and Appl. 74 (1980), 504 - 529.
    • (1980) J. Math. Anal. and Appl. , vol.74 , pp. 504-529
    • Locker, J.1    Prenter, P.M.2
  • 6
    • 4243091943 scopus 로고
    • Tikhonov regularization for finitely and infinitely smoothing operators
    • Mair, B. A.: Tikhonov regularization for finitely and infinitely smoothing operators. SIAM J. Math. Anal. 25 (1994), 135 - 147.
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 135-147
    • Mair, B.A.1
  • 7
    • 0002252004 scopus 로고
    • A survey of optimal recovery
    • (eds.: C. A. Micchelli and T. J. Rivlin). New York et al.: Plenum Press
    • Micchelli, C. A. and T. J. Rivlin: A survey of optimal recovery. In: Optimal Estimation in Approximation Theory (eds.: C. A. Micchelli and T. J. Rivlin). New York et al.: Plenum Press 1977, pp. 1 - 53.
    • (1977) Optimal Estimation in Approximation Theory , pp. 1-53
    • Micchelli, C.A.1    Rivlin, T.J.2
  • 8
    • 0000739264 scopus 로고
    • On the solution of functional equations by the method of regularization
    • Morozov, V. A.: On the solution of functional equations by the method of regularization. Soviet Math. Dokldy 7 (1966), 414 - 417.
    • (1966) Soviet Math. Dokldy , vol.7 , pp. 414-417
    • Morozov, V.A.1
  • 10
    • 0042131471 scopus 로고    scopus 로고
    • The trade-off between regularity and stability in Tikhonov regularization
    • Nair, M. T., Hegland, M. and R. S. Anderssen: The trade-off between regularity and stability in Tikhonov regularization. Mathematics of Computation 66 (1997), 193 - 206.
    • (1997) Mathematics of Computation , vol.66 , pp. 193-206
    • Nair, M.T.1    Hegland, M.2    Anderssen, R.S.3
  • 11
    • 84951418001 scopus 로고
    • Error bounds for Tikhonov regularization in Hubert scales
    • Natterer, F.: Error bounds for Tikhonov regularization in Hubert scales. Applicable Analysis 18 (1984), 29 - 37.
    • (1984) Applicable Analysis , vol.18 , pp. 29-37
    • Natterer, F.1
  • 12
    • 0010677370 scopus 로고
    • Error estimates for Tikhonov regularization in Hilbert scales
    • Schroeter, T. and U. Tautenhahn: Error estimates for Tikhonov regularization in Hilbert scales. Numer. Funct. Anal, and Optim. 15 (1994), 155 - 168.
    • (1994) Numer. Funct. Anal, and Optim. , vol.15 , pp. 155-168
    • Schroeter, T.1    Tautenhahn, U.2
  • 14
    • 0001504070 scopus 로고
    • An a posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates
    • Neubauer, A.: An a posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates. SIAM J. Numer. Anal. 25 (1988), 1313 - 1326.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1313-1326
    • Neubauer, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.