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1	Minimum Norm Regularization of Descriptor Systems by Output Feedback Chu, D., Mehrmann, V. 30 October 1998 (has links) (PDF) We study the regularization problem for linear, constant coefficient descriptor systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and $E +BG\Gamma$ has a desired rank, i.e. there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedbacks gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way. regularization mixed outputp differential and algebraic equations orthogonal matrix transformation MSC 93B05 MSC 93B40 MSC 93B52 MSC 65F35 ddc:510
2	A parallel version of the preconditioned conjugate gradient method for boundary element equations Pester, M., Rjasanow, S. 30 October 1998 (has links) (PDF) The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems. conjugate gradient algorithm fast Fourier transform preconditioning numerical experiments Galerkin boundary element method Laplace equation parallelization MSC 65N38 MSC 65F10 MSC 65Y05 MSC 65F35 MSC 35J05 ddc:510
3	A parallel preconditioned iterative realization of the panel method in 3D Pester, M., Rjasanow, S. 30 October 1998 (has links) (PDF) The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited also in three-dimensional case for implementation on a MIMD computer and that they are much more efficient than usual direct solution techniques. preconditioning parallel computation panel boundary element method iterative methods MIMD computer. MSC 65N38 MSC 65F10 MSC 35J25 MSC 65F35 MSC 65Y05 ddc:510
4	A parallel preconditioned iterative realization of the panel method in 3D Pester, M., Rjasanow, S. 30 October 1998 (has links) The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited also in three-dimensional case for implementation on a MIMD computer and that they are much more efficient than usual direct solution techniques. info:eu-repo/classification/ddc/510 ddc:510 preconditioning parallel computation panel boundary element,method iterative methods MIMD computer. MSC 65N38 MSC 65F10 MSC 35J25 MSC 65F35 MSC 65Y05
5	Minimum Norm Regularization of Descriptor Systems by Output Feedback Chu, D., Mehrmann, V. 30 October 1998 (has links) We study the regularization problem for linear, constant coefficient descriptor systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and $E +BG\Gamma$ has a desired rank, i.e. there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedbacks gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way. info:eu-repo/classification/ddc/510 ddc:510 regularization mixed outputp differential and algebraic equations orthogonal matrix transformation MSC 93B05 MSC 93B40 MSC 93B52 MSC 65F35
6	A parallel version of the preconditioned conjugate gradient method for boundary element equations Pester, M., Rjasanow, S. 30 October 1998 (has links) The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems. info:eu-repo/classification/ddc/510 ddc:510 conjugate gradient algorithm fast Fourier transform preconditioning numerical experiments Galerkin boundary element method Laplace equation parallelization MSC 65N38 MSC 65F10 MSC 65Y05 MSC 65F35 MSC 35J05

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