1,404 research outputs found
A conversation with Volker Mehrmann
No full textVolker Mehrmann is a complete mathematician excelling in all areas: research, teaching, knowledge transfer, and management. He is a specialist in numerical linear algebra, algebraic-differential equations, and control theory, and he enjoys conducting research motivated by real-world problems and developing fundamental mathematics that has a significant impact on science and technology. With a striking personality, Mehrmann leaves a remarkable legacy as former president of GAMM (International Association for Applied Mathematics and Mechanics), MATHEON (Mathematical Research Center for Key Technologies), ECMath (Einstein Center for Mathematics in Berlin), and EMS (European Mathematical Society). He is attentive to how mathematics is communicated to fellow mathematicians and to the general public, and he takes care of the working environment of his students.The three of us (Sílvia Barbeiro, Ana Isabel Mendes and Martin Raussen) held a videoconference meeting with Volker Mehrmann last October. We listened eagerly to his answers to all our questions. At the end, we discovered his secret: mathematics brings happiness
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
An inverse-free ADI algorithm for computing Lagrangian invariant subspaces
No full textSummary: The numerical computation of Lagrangian invariant subspaces of large-scale Hamiltonian matrices is discussed in the context of the solution of Lyapunov equations. A new version of the low-rank alternating direction implicit method is introduced, which, in order to avoid numerical difficulties with solutions that are of very large norm, uses an inverse-free representation of the subspace and avoids inverses of ill-conditioned matrices. It is shown that this prevents large growth of the elements of the solution that may destroy a low-rank approximation of the solution. A partial error analysis is presented, and the behavior of the method is demonstrated via several numerical examples. Copyrigh
Numerical algebra, matrix theory, differential-algebraic equations and control theory: festschrift in honor of Volker Mehrmann
No full textThis edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory
Uma Conversa com Volker Mehrmann: A Matemática traz Felicidade:Matemáticos na primeira pessoa
No full textVolker Mehrmann er en komplet matematiker og overrasker i alle aspekter: forskning, undervisning, videnoverførsel og administrative stillinger. Specialist inden for områderne numerisk lineær algebra, algebraiske differentialligninger og kontrolteori, nyder han at lave forskning motiveret af reelle problemer og udvikle virkningsfuld grundlæggende matematik inden for videnskab og teknologi.<br/
A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems
No full textConvergence 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
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Numerical methods for the regularization of descriptor systems by output feedback
No full textBunse-Gerstner, Angelika; Mehrmann, Volker; Nichols, Nancy K.. (1992). Numerical methods for the regularization of descriptor systems by output feedback. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4225
Numerical methods in control, from pole assignment via linear quadratic to H infinity control
No full textWe study classical control problems like pole assignment, stabilization, linear quadratic control and H1 control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches. AMS subject classification. 65F15, 93B40, 93B36, 93C60. Authors: Volker Mehrmann and Hongguo Xu Fakultat fur Mathematik, TU Chemnitz, D-09107 Chemnitz, FRG. Supported by Deutsche Forschungsgemeinschaft, within Sonderforschungsbereich SFB393, `Numerische Simulation auf massiv parallelen Rechnern'. 1 Introduction In the last 40 years linear systems theory (control theory) has evolved into a mature field that has found a stable position on the borderline between applied mathematics, engineering and computer science. The major success is not only due to the fact that beautiful mathematical theories (like linear algebra, ring theory, rep..
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
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