Festschrift for outstanding researcher
Discussion of selected topics of applied mathematics by unique selection of international experts
Summaries of particular theories and algorithms and discussion of their development as well as the state-of-the-art
This 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.
Related Subjects: Numerical Analysis, Computational Science and Engineering, Linear and Multilinear Algebras, Matrix Theory, Ordinary Differential Equations, Systems Theory, Control.
Author(s): Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, Tatjana Stykel
Edition: 2015
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: C, XLIV, 608
Tags: Numerical Analysis; Computational Science and Engineering; Linear and Multilinear Algebras, Matrix Theory; Ordinary Differential Equations; Systems Theory, Control
Front Matter....Pages i-xliv
Front Matter....Pages 1-1
Breaking Van Loan’s Curse: A Quest forStructure-Preserving Algorithms for Dense Structured Eigenvalue Problems....Pages 3-23
Large-Scale Structured Eigenvalue Problems....Pages 25-43
Palindromic Eigenvalue Problems in Applications....Pages 45-65
Theory and Numerical Solution of Differential and Algebraic Riccati Equations....Pages 67-105
Permuted Graph Matrices and Their Applications....Pages 107-129
Canonical Forms of Structured Matrices and Pencils....Pages 131-159
Perturbation Analysis of Matrix Equations and Decompositions....Pages 161-197
Structured Eigenvalue Perturbation Theory....Pages 199-222
A Story on Adaptive Finite Element Computations for Elliptic Eigenvalue Problems....Pages 223-255
Algebraic Preconditioning Approaches and Their Applications....Pages 257-295
Front Matter....Pages 297-297
Continuous Matrix Factorizations....Pages 299-318
Polynomial Eigenvalue Problems: Theory, Computation, and Structure....Pages 319-348
Stability in Matrix Analysis Problems....Pages 349-376
Low-Rank Approximation of Tensors....Pages 377-411
Front Matter....Pages 413-413
Regularization of Descriptor Systems....Pages 415-433
Differential-Algebraic Equations: Theory and Simulation....Pages 435-462
DAEs in Applications....Pages 463-501
A Condensed Form for Nonlinear Differential-Algebraic Equations in Circuit Theory....Pages 503-531
Spectrum-Based Robust Stability Analysis of Linear Delay Differential-Algebraic Equations....Pages 533-557
Distance Problems for Linear Dynamical Systems....Pages 559-583
Front Matter....Pages 413-413
Discrete Input/Output Maps and their Relation to Proper Orthogonal Decomposition....Pages 585-608
