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Analysis und Numerik linearer differentiellalgebraischer GleichungenKunkel, Peter, Mehrmann, Volker 30 October 1998 (has links)
In Analysis and Numerik differentialalgebraischer Gleichungen P. Kunkel and V. Mehrmann give a survey of relevant conditions for consistent systems, for existence and uniqueness of solutions, and touch numerical procedures for obtaining the solutions.

22 
GrafikAusgabe vom Parallelrechner für 3DGebieteMeyer, M. 30 October 1998 (has links)
The paper describes a method for Visualization of computational results in parallel finite element applications for 3D problems. The visualization itself is done on a workstation using a post processing tool based on GRAPE, which interacts with the parallel program to obtain data.

23 
Parallel solution of finite element equation systems: efficient interprocessor communicationApel, T., Haase, G., Meyer, A., Pester, M. 30 October 1998 (has links)
This paper deals with the application of domain decomposition methods for the parallel solution of boundary value problems for partial differential equations over a domain $Omegabset R^d$, $d=2,3$. The attention is focused on the conception of efficient communication routines for the data exchange which is necessary for example in the preconditioned cgalgorithm for solving the resulting system of algebraic equations. The paper describes the data structure, different algorithms, and computational tests.

24 
Canonical forms for linear descriptor systems with variable coefficientsRath, W. 30 October 1998 (has links)
We study linear descriptor systems with rectangular variable coefficient matrices.
Using local and global equivalence transformations we introduce normal and
condensed forms and get sets of characteristic quantities. These quantities allow us to
decide whether a linear descriptor system with variable coefficients is regularizable
by derivative and/or proportional state feedback or not. Regularizable by feedback
means for us that their exist a feedback which makes the closed loop system uniquely
solvable for every consistent initial vector.

25 
Placing plenty of poles is pretty preposterousHe, C., Laub, A. J., Mehrmann, V. 30 October 1998 (has links)
We discuss the pole placement problem for singleinput or multiinput control models of the form _x=Ax+Bu. This is the problem of determining a linear state feedback of the formu=F xsuch that in the closedloop system _x= (A+BF)x, the matrixA+BFhas a prescribed set of eigenvalues. We analyze the conditioning of this problem and show that it is an intrinsically illconditioned problem, and especially so when the system dimension is large. Thus even the best numerical methods for this problem may yield very bad results. On the other hand, we also discuss the question of whether one really needs to solve the pole placement problem. In most circum stances what is really required is stabilization or that the poles are in a specified region of the complex plane. This related problem may have much better conditioning. We demonstrate this via the example of stabilization.

26 
Kommunikationstechnologien beim parallelen vorkonditionierten SchurKomplement CGVerfahrenMeisel, M., Meyer, A. 30 October 1998 (has links)
Two alternative technologies of communication inside a parallelized ConjugateGradient algorithm are presented and compared to the well known hypercubecommunication. The amount of communication is diskussed in detail. A large range of numerical results corroborate the theoretical investigations.

27 
A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuoustime caseBenner, P., Laub, A. J., Mehrmann, V. 30 October 1998 (has links)
A collection of benchmark examples is presented for the numerical solution of continuoustime algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.

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A collection of benchmark examples for the numerical solution of algebraic Riccati equations II: Discretetime caseBenner, P., Laub, A. J., Mehrmann, V. 30 October 1998 (has links)
This is the second part of a collection of benchmark examples for the numerical solution of algebraic Riccati equations. After presenting examples for the continuoustime case in Part I, our concern in this paper is discretetime algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.

29 
Eigenvibrations of a plate with elastically attached loadSolov'ëv, Sergey I. 11 April 2006 (has links)
This paper is concerned with the investigation of the nonlinear eigenvalue problem describing the natural oscillations of a plate with a load that elastically attached to it. We study properties of eigenvalues and eigenfunctions of this eigenvalue problem and prove the existence theorem for eigensolutions. Theoretical results are illustrated by numerical experiments.

30 
Exact discretizations of twopoint boundary value problemsWindisch, G. 30 October 1998 (has links)
In the paper we construct exact threepoint discretizations of linear and nonlinear twopoint boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal Mmatrices in the linear case and Mfunctions in the nonlinear case.

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