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Item type:Publication, Access status: without files , Regularization of large scale total least squares problemsThe total least squares (TLS) method is an appropriate approach for linear systems when not only the right-hand side but also the system matrix is contaminated by some noise. For ill-posed problems regularization is necessary to stabilize the computed solutions. In this presentation we discuss two approaches for regularizing large scale TLS problems. One which is based on adding a quadratic constraint and a Tikhonov type regularization concept.Publicationtype: Conference Paper29 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Solving regularized total least squares problems based on eigenproblemsThe total least squares (TLS) method is a successful approach for linear problems if both the system matrix and the right hand side are contaminated by some noise. For ill-posed TLS problems regularization is necessary to stabilize the computed solution. In this paper we summarize two iterative methods which are based on a sequence of eigenproblems. The focus is on efficient implementation with particular emphasis on the reuse of information gained during the convergence history.Publicationtype: Journal Article144 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Detecting hyperbolic and definite matrix polynomialsHyperbolic or more generally definite matrix polynomials are important classes of Hermitian matrix polynomials. They allow for a definite linearization and can therefore be solved by a standard algorithm for Hermitian matrices. They have only real eigenvalues which can be characterized as minmax and maxmin values of Rayleigh functionals, but there is no easy way to test if a given polynomial is hyperbolic or definite or not. Taking advantage of the safeguarded iteration which converges globally and monotonically to extreme eigenvalues we obtain an efficient algorithm that identifies hyperbolic or definite polynomials and enables the transformation to an equivalent definite linear pencil. Numerical examples demonstrate the efficiency of the approach.Publicationtype: Journal Article167 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Validation of a spatially interconnected model for plane poiseuille flow transition controlA novel linearized model for the transition control problem in plane Poiseuille flow has been proposed recently. The model is based on a finite difference approach in streamwise direction and a spectral approach in wall normal direction. It is thus valid for all spatial frequencies and can be used for the synthesis of controllers for flow control problems, using recently developed ideas for spatially interconnected systems. In this paper the above model is validated in both time and frequency domain. For time domain validation, the transient energy is calculated and compared with previously published results. The frequency domain validation is based on nonlinear simulation: a sinusoidal disturbance is applied at the lower boundary and its effect at different locations of the channel are simulated. From a Fourier analysis of the simulated responses, the spatial and temporal frequency responses are obtained and compared with the linearized model. The results suggest that the model captures the dominant features of the problem and can be used for the design of spatially interconnected controllers.Publicationtype: Conference Paper31 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Global convergence of RTLSQEP : a solver of regularized total least squares problems via quadratic eigenproblemsThe total least squares (TLS) method is a successful approach for linear problems if both the matrix and the right hand side are contaminated by some noise. In a recent paper Sima, Van Huffel and Golub suggested an iterative method for solving regularized TLS problems, where in each iteration step a quadratic eigenproblem has to be solved. In this paper we prove its global convergence, and we present an efficient implementation using an iterative projection method with thick updates.Publicationtype: Journal ArticleScopus© Citations 17 268 271 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A new justification of the Jacobi–Davidson method for large eigenproblems(2006-04)Voß, HeinrichThe Jacobi–Davidson method is known to converge at least quadratically if the correction equation is solved exactly, and it is common experience that the fast convergence is maintained if the correction equation is solved only approximately. In this note we derive the Jacobi–Davidson method in a way that explains this robust behavior.Publicationtype: PreprintScopus© Citations 21 485 456 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Projection methods for nonlinear sparse eigenvalue problems(2006-02)Voß, HeinrichThis paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.Publicationtype: Working Paper375 416 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Reducing huge gyroscopic eigenproblems by automated multi-level substructuring(2006-01)Scopus© Citations 15 730 451