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- D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann
- SIAM J. Matrix Analysis Applications
- 2006

The classical approach to investigating polynomial eigenvalue problems is linearization, where the polynomial is converted into a larger matrix pencil with the same eigenvalues. For any polynomial there are infinitely many linearizations with widely varying properties, but in practice the companion forms are typically used. However, these companion forms… (More)

- Volker Mehrmann, David Watkins
- SIAM J. Scientific Computing
- 2001

We study large, sparse generalized eigenvalue problems for matrix pencils, where one of the matrices is Hamiltonian and the other skew Hamiltonian. Problems of this form arise in the numerical simulation of elastic deformation of anisotropic materials, in structural mechanics and in the linear-quadratic control problem for partial diierential equations. We… (More)

- D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann
- SIAM J. Matrix Analysis Applications
- 2006

Many applications give rise to nonlinear eigenvalue problems with an underlying structured matrix polynomial. In this paper several useful classes of structured polynomial (e.g., palindromic, even, odd) are identified and the relationships between them explored. A special class of linearizations that reflect the structure of these polynomials, and therefore… (More)

For the solution of the single-input pole placement problem we derive explicit expressions for the feedback gain matrix as well as the eigenvector matrix of the closed-loop system. Based on these formulas we study the conditioning of the pole-placement problem in terms of perturbations in the data and show how the conditioning depends on the condition… (More)

- Peter Benner, Volker Mehrmann, Sabine Van Hu, András Varga
- 2008

This article describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Around a nucleus of basic numerical linear algebra subroutines, this library builds methods for the design and analysis of linear control systems. A brief history of the library is given… (More)

In this paper we give a survey on balanced truncation model order reduction for linear time-invariant continuous-time systems in descriptor form. We first give a brief overview of the basic concepts from linear system theory and then present balanced truncation model reduction methods for descriptor systems and discuss their algorithmic aspects. The… (More)

- Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder, Françoise Tisseur
- ACM Trans. Math. Softw.
- 2013

We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed specifically to have particular properties. A classification is given of polynomial eigenvalue problems according to their structural properties. Identifiers based on… (More)

This paper extends the singular value decomposition to a path of matrices E(t). An analytic singular value decomposition of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t)T where X(t) and Y (t) are orthogonal and S(t) is diagonal. To maintain di erentiability the diagonal entries of S(t) are allowed to be either positive… (More)

For a general class of nonlinear (possibly higher index) di erential-algebraic equations we show existence and uniqueness of solutions. These solutions are regular in the sense that Newton's method will converge locally and quadratically. On the basis of the presented theoretical results, numerical methods for the determination of consistent initial values… (More)

- Peter Kunkel, Volker Mehrmann
- MCSS
- 2001