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Fast solution of elliptic control problems. (English) Zbl 0417.49041


MSC:

49M25 Discrete approximations in optimal control
49J20 Existence theories for optimal control problems involving partial differential equations
35J99 Elliptic equations and elliptic systems
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[1] Hackbusch, W.,On the Fast Solving of Parabolic Boundary Control Problems, SIAM Journal on Control and Optimization, Vol. 17, pp. 231-244, 1979. · Zbl 0402.49025 · doi:10.1137/0317018
[2] Lions, J. L., andMagenes, E.,Nonhomogeneous Boundary-Value Problems and Applications, Vol. 1, Springer-Verlag, Berlin, Germany, 1972.
[3] Lions, J. L.,Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, Germany, 1971. · Zbl 0203.09001
[4] Hackbusch, W.,Die schnelle Auflösung der Fredholmschen Integralgleichung zweiter Art, Beiträge zur Numerischen Mathematik (to appear). · Zbl 0458.65108
[5] Buneman, O.,A Compact Noniterative Poisson Solver, Stanford University, Institute for Plasma Research, SUIPR Report No. 294, 1969. · Zbl 0219.68055
[6] Schröder, J., andTrottenberg, U.,Reduktionsverfahren für Differenzengleichungen bei Randwertaufgaben, I, Numerische Mathematik, Vol. 22, pp. 37-68, 1973. · doi:10.1007/BF01436620
[7] Schröder, J., Trottenberg, U., andWitsch, K.,On Fast Poisson Solvers and Applications, Numerical Treatment of Differential Equations, Edited by R. Bulirsch, R. D. Grigorieff, and J. Schröder, Springer-Verlag, Berlin, Germany, 1978. · Zbl 0373.65053
[8] Hackbusch, W.,On the Multigrid Method Applied to Difference Equations, Computing, Vol. 20, pp. 291-306, 1978. · Zbl 0391.65045 · doi:10.1007/BF02252378
[9] Hackbusch, W.,A Multigrid Method Applied to a Boundary-Value Problem with Variable Coefficients in a Rectangle, Universität zu Köln, Mathematisches Institut, Report No. 77-17, 1977.
[10] Hackbusch, W.,On the Fast Solution of Nonlinear Elliptic Equations, Numerische Mathematik, Vol. 32, pp. 83-95, 1979. · doi:10.1007/BF01397652
[11] Hackbusch, W.,An Error Analysis of the Nonlinear Multigrid Method of the Second Kind, Aplikace Matematiky (to appear). · Zbl 0465.65055
[12] Hackbusch, W.,Numerical Solution of Linear and Nonlinear Parabolic Control Problems, Optimierung und optimale Steuerungen, Edited by A. Auslender, W. Oettli, and J. Stoer (to appear).
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