Angelika Bunse-Gerstner

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We present a Jacobi-like algorithm for simultaneous diagonalization of commuting pairs of complex normal matrices by unitary similarity transformations. The algorithm uses a sequence of similarity transformations by elementary complex rotations to drive the oo-diagonal entries to zero. We show that its asymptotic convergence rate is quadratic and that it is(More)
Modeling strategies often result in dynamical systems of very high dimension. It is then desirable to find systems of the same form but of lower complexity, whose input-output behavior approximates the behavior of the original system. Here we consider linear time invariant (LTI) discrete time dynamical systems. The cornerstone of this paper is a relation(More)
Unitary matrices have a rich mathematicalstructure which is closely analogous to real symmetric matrices. For real symmetric matrices this structure can be exploited to develop very eecient numerical algorithms and for some of these algorithms unitary analogues are known. Here we present a unitary analogue of the bisection method for symmetric tridiagonal(More)
When solving the Electric or Combined Field Integral Equation (EFIE or CFIE) using the Multilevel Fast Multipole Method (MLFMM), iterative solver have to be useed for the solution of the resulting very large system of linear equations, because the MLFMM provides a matrix-vector product only. It is essential to combine the iterative method with a suitable(More)
Error bounds for the eigenvalues computed in the isometric Arnoldi method are derived. The Arnoldi method applied to a unitary matrix U successively computes a sequence of unitary upper Hessenberg matrices H k ; k = 1; 2; : : :. The eigenvalues of the H k 's are increasingly better approximations to eigenvalues of U. An upper bound for the distance of the(More)
Some aspects of the perturbation theory for eigenvalues of unitary matrices are considered. Making use of the close relation between unitary and Hermitian eigenvalue problems a Courant-Fischer-type theorem for unitary matrices is derived and an inclusion theorem analogue to the Kahan theorem for Hermitian matrices is presented. Implications for the special(More)
In data assimilation applications using ensemble Kalman filter methods, localization is necessary to make the method work with high-dimensional geophysical models. For ensemble square-root Kalman filters, domain localization (DL) and observation localization (OL) are commonly used. Depending on the localization method, one has to choose appropriate values(More)
This paper deals with H 2-norm optimal model reduction for linear time invariant continuous MIMO systems. We will give an overview on several representations of linear systems in state space as well as in Laplace space and discuss the H 2-norm for continuous MIMO systems with multiple poles. On this basis, necessary optimality conditions for the H 2-norm(More)