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


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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