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Volumn 23, Issue 5, 2007, Pages 1943-1961

The balancing principle for the regularization of elliptic Cauchy problems

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE SYSTEMS; CONVERGENCE OF NUMERICAL METHODS; LINEARIZATION; PROBLEM SOLVING;

EID: 41449109255     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/5/009     Document Type: Article
Times cited : (18)

References (33)
  • 1
    • 33746272877 scopus 로고    scopus 로고
    • On Cauchy's problem: II. Completion, regularization and approximation
    • Azaez M, Ben Belgacem F and El Fekih H 2006 On Cauchy's problem: II. Completion, regularization and approximation Inverse Problems 22 1307-36
    • (2006) Inverse Problems , vol.22 , Issue.4 , pp. 1307-1336
    • Azaez, M.1    Ben Belgacem, F.2    El Fekih, H.3
  • 2
    • 31844434943 scopus 로고    scopus 로고
    • Solving Cauchy problems by minimizing an energy-like functional
    • Andrieux S, Baranger T N and Ben Abda A 2006 Solving Cauchy problems by minimizing an energy-like functional Inverse Problems 22 115-33
    • (2006) Inverse Problems , vol.22 , Issue.1 , pp. 115-133
    • Andrieux, S.1    Baranger, T.N.2    Ben Abda, A.3
  • 3
    • 33645309035 scopus 로고    scopus 로고
    • Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems
    • Baskar S and Prasad P 2006 Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems Proc. Indian Acad. Sci. Math. Sci. 116 97-119
    • (2006) Proc. Indian Acad. Sci. Math. Sci. , vol.116 , pp. 97-119
    • Baskar, S.1    Prasad, P.2
  • 4
    • 28544445998 scopus 로고    scopus 로고
    • On Cauchy's problem: I. A variational Steklov-Poincaré theory
    • Ben Belgacem F and El Fekih H 2005 On Cauchy's problem: I. A variational Steklov-Poincaré theory Inverse Problems 21 1915-36
    • (2005) Inverse Problems , vol.21 , Issue.6 , pp. 1915-1936
    • Ben Belgacem, F.1    El Fekih, H.2
  • 5
    • 3843145156 scopus 로고    scopus 로고
    • Bases of exponentials, cosines, and sines formed by eigenfunctions of differential operators
    • Bilalov B T 2003 Bases of exponentials, cosines, and sines formed by eigenfunctions of differential operators Diff. Eqns 39 652-7
    • (2003) Diff. Eqns , vol.39 , Issue.5 , pp. 652-657
    • Bilalov, B.T.1
  • 6
    • 0343772980 scopus 로고    scopus 로고
    • Numerical solution of a Cauchy problem for the Laplace equation
    • Berntsson F and Eldén L 2001 Numerical solution of a Cauchy problem for the Laplace equation Inverse Problems 17 839-53 (Special issue to celebrate Pierre Sabatier's 65th birthday (Montpellier, 2000))
    • (2001) Inverse Problems , vol.17 , Issue.4 , pp. 839-853
    • Berntsson, F.1    Eldén, L.2
  • 7
    • 33645303206 scopus 로고    scopus 로고
    • Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
    • Bourgeois L 2006 Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation Inverse Problems 22 413-30
    • (2006) Inverse Problems , vol.22 , Issue.2 , pp. 413-430
    • Bourgeois, L.1
  • 8
    • 18744373648 scopus 로고    scopus 로고
    • A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
    • Bourgeois L 2005 A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation Inverse Problems 21 1087-104
    • (2005) Inverse Problems , vol.21 , Issue.3 , pp. 1087-1104
    • Bourgeois, L.1
  • 9
    • 0037272436 scopus 로고    scopus 로고
    • Self-regularization of projection methods with a posteriori discretization level choice for severely ill-posed problems
    • Bruckner G and Pereverzev S V 2003 Self-regularization of projection methods with a posteriori discretization level choice for severely ill-posed problems Inverse Problems 19 147-56
    • (2003) Inverse Problems , vol.19 , Issue.1 , pp. 147-156
    • Bruckner, G.1    Pereverzev, S.V.2
  • 10
    • 0001191809 scopus 로고    scopus 로고
    • Stability for an inverse boundary problem of determining a part of a boundary
    • Bukhgeim A L, Cheng J and Yamamoto M 1999 Stability for an inverse boundary problem of determining a part of a boundary Inverse Problems 15 1021-32
    • (1999) Inverse Problems , vol.15 , Issue.4 , pp. 1021-1032
    • Bukhgeim, A.L.1    Cheng, J.2    Yamamoto, M.3
  • 11
    • 33746287735 scopus 로고    scopus 로고
    • Convergence analysis for finite element approximation to an inverse Cauchy problem
    • Chakib A and Nachaoui A 2006 Convergence analysis for finite element approximation to an inverse Cauchy problem Inverse Problems 22 1191-206
    • (2006) Inverse Problems , vol.22 , Issue.4 , pp. 1191-1206
    • Chakib, A.1    Nachaoui, A.2
  • 12
    • 0035363955 scopus 로고    scopus 로고
    • Solution of the Cauchy problem using iterated Tikhonov regularization
    • Cimetière A, Delvare F, Jaoua M and Pons F 2001 Solution of the Cauchy problem using iterated Tikhonov regularization Inverse Problems 17 553-70
    • (2001) Inverse Problems , vol.17 , Issue.3 , pp. 553-570
    • Cimetière, A.1    Delvare, F.2    Jaoua, M.3    Pons, F.4
  • 14
    • 0035518988 scopus 로고    scopus 로고
    • A Mann iterative regularization method for elliptic Cauchy problems
    • Engl H W and Leito A 2001 A Mann iterative regularization method for elliptic Cauchy problems Numer. Funct. Anal. Optim. 22 861-84
    • (2001) Numer. Funct. Anal. Optim. , vol.22 , Issue.7-8 , pp. 861-884
    • Engl, H.W.1    Leito, A.2
  • 16
    • 0022360366 scopus 로고
    • A mathematical procedure for solving the inverse potential problem of electrocardiography. Analysis of the time-space accuracy from in vitro experimental data
    • Franzone Colli P, Guerri L, Tentoni S, Viganotti C, Baruffi S, Spaggiari S and Taccardi B 1985 A mathematical procedure for solving the inverse potential problem of electrocardiography. Analysis of the time-space accuracy from in vitro experimental data Math. Biosci. 77 353-96
    • (1985) Math. Biosci. , vol.77 , Issue.1-2 , pp. 353-396
    • Franzone Colli, P.1    Guerri, L.2    Tentoni, S.3    Viganotti, C.4    Baruffi, S.5    Spaggiari, S.6    Taccardi, B.7
  • 17
    • 51249182572 scopus 로고
    • On the inverse potential problem of electrocardiology
    • Franzone Colli P and Magenes E 1979 On the inverse potential problem of electrocardiology Calcolo 16 459-538
    • (1979) Calcolo , vol.16 , Issue.4 , pp. 459-538
    • Franzone Colli, P.1    Magenes, E.2
  • 19
    • 0013018579 scopus 로고
    • Convergence of a general projection method for an operator equation of the first kind
    • Groetsch C W and Neubauer A 1988 Convergence of a general projection method for an operator equation of the first kind Houston J. Math. 14 201-08
    • (1988) Houston J. Math. , vol.14 , pp. 201-208
    • Groetsch, C.W.1    Neubauer, A.2
  • 20
    • 0041691885 scopus 로고    scopus 로고
    • Some stability estimates for Cauchy problems for elliptic equations
    • Han H and Reinhardt H J 1997 Some stability estimates for Cauchy problems for elliptic equations J. Inverse Ill-Posed Probl. 5 437-54
    • (1997) J. Inverse Ill-Posed Probl. , vol.5 , pp. 437-454
    • Han, H.1    Reinhardt, H.J.2
  • 21
    • 0035306176 scopus 로고    scopus 로고
    • Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
    • Hon Y C and Wei T 2001 Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation Inverse Problems 17 261-71
    • (2001) Inverse Problems , vol.17 , Issue.2 , pp. 261-271
    • Hon, Y.C.1    Wei, T.2
  • 23
    • 0041734177 scopus 로고    scopus 로고
    • Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems
    • Kaltenbacher B 2000 Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems Inverse Problems 16 1523-39
    • (2000) Inverse Problems , vol.16 , Issue.5 , pp. 1523-1539
    • Kaltenbacher, B.1
  • 24
    • 0742288818 scopus 로고    scopus 로고
    • Mean value iterations for nonlinear elliptic Cauchy problems
    • Kügler P and Leito A 2003 Mean value iterations for nonlinear elliptic Cauchy problems Numer. Math. 96 269-93
    • (2003) Numer. Math. , vol.96 , Issue.2 , pp. 269-293
    • Kügler, P.1    Leito, A.2
  • 25
    • 41449111988 scopus 로고    scopus 로고
    • On the balancing principle for some problems of numerical analysis
    • Lazarov R D, Lu S and Pereverzyev S V 2005 On the balancing principle for some problems of numerical analysis RICAM Report 25 (Austria: RICAM)
    • (2005) RICAM Report
    • Lazarov, R.D.1    Lu, S.2    Pereverzyev, S.V.3
  • 26
    • 0034250874 scopus 로고    scopus 로고
    • An iterative method for solving elliptic Cauchy problems
    • Leito A 2000 An iterative method for solving elliptic Cauchy problems Numer. Funct. Anal. Optim. 21 715-42
    • (2000) Numer. Funct. Anal. Optim. , vol.21 , Issue.5 , pp. 715-742
    • Leito, A.1
  • 27
    • 0347557399 scopus 로고
    • Convergence of approximate solutions of an operator equation
    • Luecke G R and Hickey K R 1985 Convergence of approximate solutions of an operator equation Houston J. Math. 11 345-54
    • (1985) Houston J. Math. , vol.11 , pp. 345-354
    • Luecke, G.R.1    Hickey, K.R.2
  • 28
    • 0346946904 scopus 로고    scopus 로고
    • Discretization strategy for linear ill-posed problems in variable Hilbert scales
    • Mathé P and Pereverzev S V 2003 Discretization strategy for linear ill-posed problems in variable Hilbert scales Inverse Problems 19 1263-77
    • (2003) Inverse Problems , vol.19 , Issue.6 , pp. 1263-1277
    • Mathé, P.1    Pereverzev, S.V.2
  • 29
    • 0000363718 scopus 로고
    • Regularisierung schlecht gestellter Probleme durch Projektionsverfahren
    • Natterer F 1977 Regularisierung schlecht gestellter Probleme durch Projektionsverfahren Numer. Math. 28 329-41 (in German)
    • (1977) Numer. Math. , vol.28 , Issue.3 , pp. 329-341
    • Natterer, F.1
  • 30
    • 4644355279 scopus 로고
    • Operator ideals
    • Pietsch A 1978 Operator ideals Mathematische Monographien (Mathematical Monographs vol 16) (Berlin: VEB Deutscher Verlag der Wissenschaften) p 451
    • (1978) Mathematische Monographien , pp. 451
    • Pietsch, A.1
  • 31
    • 0001189418 scopus 로고    scopus 로고
    • Stability and regularization of a discrete approximation to the Cauchy problem for Laplace's equation
    • Reinhardt H J, Han H and Ho D H 1999 Stability and regularization of a discrete approximation to the Cauchy problem for Laplace's equation SIAM J. Numer. Anal. 36 890-905 (electronic)
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.3 , pp. 890-905
    • Reinhardt, H.J.1    Han, H.2    Ho, D.H.3
  • 32
    • 0008522406 scopus 로고
    • Nonconvergence results for the application of least-squares estimation to ill-posed problems
    • Seidman T I 1980 Nonconvergence results for the application of least-squares estimation to ill-posed problems J. Optim. Theory Appl. 30 535-47
    • (1980) J. Optim. Theory Appl. , vol.30 , Issue.4 , pp. 535-547
    • Seidman, T.I.1
  • 33
    • 21444446911 scopus 로고    scopus 로고
    • Optimal stable solution of Cauchy problems for elliptic equations
    • Tautenhahn U 1996 Optimal stable solution of Cauchy problems for elliptic equations Z. Anal. Anwendungen 15 961-84
    • (1996) Z. Anal. Anwendungen , vol.15 , pp. 961-984
    • Tautenhahn, U.1


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