Volker Mehrmann

Peter Benner

Danny C. Sorensen

In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

Proceedings of a Workshop held in Oberwolfach, Germany, October 19-25, 2003

Dimension Reduction of Large-Scale Systems

Peter Kunkel

This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems.

Analysis and Numerical Solution

Differential-algebraic Equations

Vadim Olshevsky

Dario Andrea Bini

Eugene Tyrtsyhnikov

Marc van Barel

This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.

The Georg Heinig Memorial Volume

Numerical Methods for Structured Matrices and Applications

Jörg Liesen

Eine Einführung, welche die Lineare Algebra aus Anwendungsproblemen motiviert und eine Basis- und Matrizenorientierte Darstellung mit der abstrakten mathematischen Theorie kombiniert. Die Bedeutung der Linearen Algebra für die Entwicklung moderner numerischer Verfahren sowie als grundlegendes Werkzeug im Bereich der reinen Mathematik wird verdeutlicht. Das Buch ist stark modularisiert und für unterschiedliche Typen von Lehrveranstaltungen geeignet.

Ein Lehrbuch über die Theorie mit Blick auf die Praxis

Lineare Algebra

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.

Linear Algebra

Wolfgang Arendt

Jussi Behrndt

Joseph A. Ball

Karl-Heinz Förster

Carsten Trunk

The present volume contains a collection of original research articles and expository contributions on recent developments in operator theory and its multifaceted applications. They cover a wide range of themes from the IWOTA 2010 conference held at the TU Berlin, Germany, including spectral theory, function spaces, mathematical system theory, evolution equations and semigroups, and differential and difference operators. The book encompasses new trends and various modern topics in operator theory, and serves as a useful source of information to mathematicians, scientists and engineers.

21st International Workshop on Operator Theory and Applications, Berlin, July 2010

Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

Martin Grötschel

Klaus Lucas

Mathematik trägt immer stärker zur Produktentwicklung und Produktionssicherheit, zur Wertschöpfung und Ressourcenschonung bei. Das Buch erörtert in verschiedenen ingenieurwissenschaftlichen Themenfeldern das Verhältnis von Mathematik und Technikwissenschaften, den Beitrag der Mathematik zur industriellen Wertschöpfung und die Schlüsselrolle der Mathematik bei der Beherrschung komplexer Systeme. Gleichzeitig schlagen die Autoren Maßnahmen zur Verbesserung der Interaktion zwischen Mathematik und Technikwissenschaften, Forschung und Industrie vor.

Produktionsfaktor Mathematik

Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like How can mathematics improve to the improvement of technological processes and products? What is happening already? Where are the deficits? What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering.

Volker Mehrmann

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