112,015 research outputs found
An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems
No full textAbstractA new implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric generalized eigenvalue problems is presented. The new method improves and generalizes the SHIRA method of Mehrmann and Watkins (2001) [37] to the case where the skew-symmetric matrix is singular. It computes a few eigenvalues and eigenvectors of the matrix pencil close to a given target point. Several applications from control theory are presented and the properties of the new method are illustrated by benchmark examples
Minimizing the condition number of a positive definite matrix by completion
No full textElsner L, He C, Mehrmann V. Minimizing the condition number of a positive definite matrix by completion. Numerische Mathematik. 1994;69(1):17-23.We consider the problem of minimizing the spectral condition number of a positive definite matrix by completion: [GRAPHICS] where A is an n x n Hermitian positive definite matrix, B a p x n matrix and X is a free p x p Hermitian matrix. We reduce this problem to an optimization problem for a convex function in one variable. Using the minimal solution of this problem we characterize the complete set of matrices that give the minimum condition number
On the LU decomposition of V-matrices
No full textAbstractWe show that the class of V-matrices, introduced by Mehrmann [6], which contains the M-matrices and the Hermitian positive semidefinite matrices, is invariant under Gaussian elimination
Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations
No full textElsner L, Mehrmann V. Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations. Numerische Mathematik. 1991;59(1):541-559.We discuss block matrices of the form A = [A(ij)], where A(ij) is a k x k symmetric matrix, A(ii) is positive definite and A(ij) is negative semidefinite. These matrices are natural block-generalizations of Z-matrices and M-matrices. Matrices of this type arise in the numerical solution of Euler equations in fluid flow computations. We discuss properties of these matrices, in particular we prove convergence of block iterative methods for linear systems with such system matrices
On classes of matrices containing M-matrices, totally nonnegative and hermitian positive semidefinite matrices
No full textMehrmann V. On classes of matrices containing M-matrices, totally nonnegative and hermitian positive semidefinite matrices. Bielefeld; 1982
Priority Vectors for Matrices of pairwise Comparisons
No full textElsner L, Mehrmann V. Priority Vectors for Matrices of pairwise Comparisons. Methods of Operations Research. 1989;58:15-26
Using permuted graph bases in H-infinity control
No full textWe present a new numerical method (based on the computation of deflating subspaces) for the γ-iteration in H∞ control in the extended matrix pencil formulation. We introduce a permuted graph representation of these subspaces, which avoids the known difficulties that arise when the iteration is based on the solution of algebraic Riccati equations but at the same time makes use of the special symmetry structures that are present in the problems. We use this representation to perform both the deflation of spurious ∞ eigenvalues of the even pencils and the implementation of the inverse-free sign iteration. We show that the new method returns accurate results and is applicable in many situations where conventional methods fail. © 2013 Elsevier Ltd. All rights reserved
Analysis und Numerik linearer differentiell-algebraischer Gleichungen
No full textIn Analysis and Numerik differential-algebraischer 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
A new block method for computing the Hamiltonian Schur form
No full textAbstractA generalization of the method of Chu et al. [D. Chu, X. Liu, V. Mehrmann, A numerical method for computing the Hamiltonian Schur form. Numer. Math. 105 (2007) 375–412]. for the computation of the Hamiltonian real Schur form is presented. The new method avoids some of the difficulties that may arise when a Hamiltonian matrix has tightly clustered groups of eigenvalues. A detailed analysis of the method is presented and several numerical examples demonstrate the superior behavior of the method
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