Titlebook: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory; Festschrift in Honor Peter Benner,Matthias Bollhöfer

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Large-Scale Structured Eigenvalue Problems transformed to symplectic or skew-Hamiltonian problems and then solved. This chapter focuses on the transformation to skew-Hamiltonian form and solution by the SHIRA method. Related to, but more general than, Hamiltonian matrices are alternating and palindromic pencils. A SHIRA-like method that ope

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Theory and Numerical Solution of Differential and Algebraic Riccati Equations in many computational methods for solving problems in systems and control theory, like controller design, Kalman filtering, model reduction, and many more. We will review some basic theoretical facts as well as computational methods to solve them, with a special emphasis on the many contributions V

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Canonical Forms of Structured Matrices and Pencilshe investigation of application problems. The survey mainly focuses on the results from three topics that have been developed during the past 15 years: structured canonical forms for Hamiltonian and related matrices, structured canonical forms for doubly structured matrices and pencils, and singular

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Perturbation Analysis of Matrix Equations and Decompositionsents are the desired solutions. If a particular data is perturbed then the corresponding solution is also perturbed. The goal of the norm-wise perturbation analysis is to estimate the norm of the perturbation in the solution as a function of the norms of the perturbations in the data. In turn, in th

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A Story on Adaptive Finite Element Computations for Elliptic Eigenvalue Problemsjoint partial differential equations (PDEs). The main goal of this paper is to present the variety of subjects and corresponding results contributing to this very complex and broad area of research, and to provide a reader with a relevant sources of information for further investigations.

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Algebraic Preconditioning Approaches and Their Applicationsble for solving linear systems in parallel. We will also demonstrate how completion techniques can serve as a useful tool to prevent ill-conditioned systems. Beside parallel aspects for preconditioning, multilevel factorization methods will be investigated and finally we will demonstrate how these m

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Continuous Matrix Factorizationsing particular attention to smooth matrix factorizations of fundamental matrix solutions of linear differential equations and differential-algebraic equations with special emphasis on smooth QR and smooth SVD.

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Stability in Matrix Analysis Problemse called stable with respect to . and the collection ., if for every . which is sufficiently close to .. there exists an element . that is as close to .. as we wish. Give criteria for existence of a stable .., and describe all of them. 2. Fix . ≥ 1. An element . will be called .-stable with respect