Abstract
In this paper we establish a convergence rate result for a parameter identification problem. We show that the convergence rate of a convection parameter in an elliptic equation with Dirichlet boundary conditions is \( \mathcal{O}\left( {\sqrt \delta } \right) \) , where δ is a norm bound for the noise in the data.
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Colonius, F., Kunisch, K.: Stability for parameter estimation in two point boundary value problems. J. Reine Angewandte Math. 370 (1986) 1–29
Engl, H. W.: Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates. J. Opt. Theor. Appl. 52 (1987) 209–215
Engl, H. W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer Academic Publishers (1996)
Engl, H. W., Kunisch, K., Neubauer, A.: Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems. Inverse Problems 5 (1989) 523–540
Hou, Z., Yang, H.: Convergence rates of regularized solutions of nonlinear ill-posed operator equations involving monotone operators. Science in China (Series A) 41 No. 3 (1998) 252–259
Kravaris, C. Seinfeld, J. H.: Identification of parameters in distributed parameter systems by regularization. SIAM J. Control Opt. 23 (1985) 217–241
Kunisch, K, White, L. W.: Parameter estimations, regularity and the penalty method for a class of two point boundary value problems. SIAM J. Control and Optimization 25 No. 1 (1987) 100–120
Neubauer, A.: Tikhonov regularisation for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation. Inverse Problems 5 (1989) 541–667
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© 2001 Springer-Verlag Berlin Heidelberg
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Dimitriu, G. (2001). Convergence Rate for a Convection Parameter Identified Using Tikhonov Regularization. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_30
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DOI: https://doi.org/10.1007/3-540-45262-1_30
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