Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations.
George, Santhosh, Nair, M.Thamban (2004)
International Journal of Mathematics and Mathematical Sciences
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George, Santhosh, Nair, M.Thamban (2004)
International Journal of Mathematics and Mathematical Sciences
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Zbigniew Leyk (1990)
Numerische Mathematik
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Fu, Chu-Li, Li, Hong-Fang, Xiong, Xiang-Tuan, Fu, Peng (2005)
International Journal of Mathematics and Mathematical Sciences
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E.F. D'Azevedo, R.B. Simpson (1991)
Numerische Mathematik
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K. Scherer (1980/81)
Numerische Mathematik
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Osipenko, K.Yu. (2003)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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A. G. Sukharev (1984)
Banach Center Publications
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Round-off error analysis of the gradient method.
Gabriel N. Gatica (1987)
Extracta Mathematicae
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Luca Dede', Alfio Quarteroni (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates...
Ludwig Kohaupt (1987/88)
Numerische Mathematik
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Ludwig Kohaupt (1986/87)
Numerische Mathematik
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Mark Kärcher, Martin A. Grepl (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...