Contributions To The Numerical Solution Of Algebraic Riccati Equations And Related Eigenvalue Problems
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Contributions To The Numerical Solution Of Algebraic Riccati Equations And Related Eigenvalue Problems
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Author : Peter Benner
language : en
Publisher:
Release Date : 1997
Contributions To The Numerical Solution Of Algebraic Riccati Equations And Related Eigenvalue Problems written by Peter Benner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Eigenvalues categories.
Numerical Algebra Matrix Theory Differential Algebraic Equations And Control Theory
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Author : Peter Benner
language : en
Publisher: Springer
Release Date : 2015-05-09
Numerical Algebra Matrix Theory Differential Algebraic Equations And Control Theory written by Peter Benner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-09 with Mathematics categories.
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.
Proceedings Of The Conference On Applied Mathematics And Scientific Computing
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Author : Zlatko Drmac
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Proceedings Of The Conference On Applied Mathematics And Scientific Computing written by Zlatko Drmac and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Mathematics categories.
This book brings together contributed papers presenting new results covering different areas of applied mathematics and scientific computing. Firstly, four invited lectures give state-of-the-art presentations in the fields of numerical linear algebra, shape preserving approximation and singular perturbation theory. Then an overview of numerical solutions to skew-Hamiltonian and Hamiltonian eigenvalue problems in system and control theory is given by Benner, Kressner and Mehrmann. The important issue of structure preserving algorithms and structured condition numbers is discussed. Costantini and Sampoli review the basic ideas of the abstract schemes and show that they can be used to solve any problem concerning the construction of spline curves subject to local constraints. Kvasov presents a novel approach in solving the problem of shape preserving spline interpolation. Formulating this problem as a differential multipoint boundary value problem for hyperbolic and biharmonic tension splines he considers its finite difference approximation. Miller and Shishkin consider the Black-Scholes equation that, for some values of the parameters, may be a singularly perturbed problem. They construct a new numerical method, on an appropriately fitted piecewise-uniform mesh, which is parameter-uniformly convergent.
Perturbation Theory For Matrix Equations
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Author : M. Konstantinov
language : en
Publisher: Gulf Professional Publishing
Release Date : 2003-05-20
Perturbation Theory For Matrix Equations written by M. Konstantinov and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-20 with Mathematics categories.
The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis. In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds. Key features: • The first book in this field • Can be used by a variety of specialists • Material is self-contained • Results can be used in the development of reliable computational algorithms • A large number of examples and graphical illustrations are given • Written by prominent specialists in the field
Approximate Solution Of Non Symmetric Generalized Eigenvalue Problems And Linear Matrix Equations On Hpc Platforms
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Author : Martin K"ohler
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2022-01-18
Approximate Solution Of Non Symmetric Generalized Eigenvalue Problems And Linear Matrix Equations On Hpc Platforms written by Martin K"ohler and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-18 with Mathematics categories.
The solution of the generalized eigenvalue problem is one of the computationally most challenging operations in the field of numerical linear algebra. A well known algorithm for this purpose is the QZ algorithm. Although it has been improved for decades and is available in many software packages by now, its performance is unsatisfying for medium and large scale problems on current computer architectures. In this thesis, a replacement for the QZ algorithm is developed. The design of the new spectral divide and conquer algorithms is oriented towards the capabilities of current computer architectures, including the support for accelerator devices. The thesis describes the co-design of the underlying mathematical ideas and the hardware aspects. Closely connected with the generalized eigenvalue value problem, the solution of Sylvester-like matrix equations is the concern of the second part of this work. Following the co-design approach, introduced in the first part of this thesis, a flexible framework covering (generalized) Sylvester, Lyapunov, and Stein equations is developed. The combination of the new algorithms for the generalized eigenvalue problem and the Sylvester-like equation solves problems within an hour, whose solution took several days incorporating the QZ and the Bartels-Stewart algorithm.
Numerical Linear Algebra In Signals Systems And Control
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Author : Paul Van Dooren
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-21
Numerical Linear Algebra In Signals Systems And Control written by Paul Van Dooren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-21 with Technology & Engineering categories.
The purpose of Numerical Linear Algebra in Signals, Systems and Control is to present an interdisciplinary book, blending linear and numerical linear algebra with three major areas of electrical engineering: Signal and Image Processing, and Control Systems and Circuit Theory. Numerical Linear Algebra in Signals, Systems and Control will contain articles, both the state-of-the-art surveys and technical papers, on theory, computations, and applications addressing significant new developments in these areas. The goal of the volume is to provide authoritative and accessible accounts of the fast-paced developments in computational mathematics, scientific computing, and computational engineering methods, applications, and algorithms. The state-of-the-art surveys will benefit, in particular, beginning researchers, graduate students, and those contemplating to start a new direction of research in these areas. A more general goal is to foster effective communications and exchange of information between various scientific and engineering communities with mutual interests in concepts, computations, and workable, reliable practices.
Applied And Computational Control Signals And Circuits
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Author : Biswa N. Datta
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied And Computational Control Signals And Circuits written by Biswa N. Datta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The purpose of this annual series, Applied and Computational Control, Signals, and Circuits, is to keep abreast of the fast-paced developments in computational mathematics and scientific computing and their increasing use by researchers and engineers in control, signals, and circuits. The series is dedicated to fostering effective communication between mathematicians, computer scientists, computational scientists, software engineers, theorists, and practicing engineers. This interdisciplinary scope is meant to blend areas of mathematics (such as linear algebra, operator theory, and certain branches of analysis) and computational mathematics (numerical linear algebra, numerical differential equations, large scale and parallel matrix computations, numerical optimization) with control and systems theory, signal and image processing, and circuit analysis and design. The disciplines mentioned above have long enjoyed a natural synergy. There are distinguished journals in the fields of control and systems the ory, as well as signal processing and circuit theory, which publish high quality papers on mathematical and engineering aspects of these areas; however, articles on their computational and applications aspects appear only sporadically. At the same time, there has been tremendous recent growth and development of computational mathematics, scientific comput ing, and mathematical software, and the resulting sophisticated techniques are being gradually adapted by engineers, software designers, and other scientists to the needs of those applied disciplines.
Structured Matrices In Mathematics Computer Science And Engineering I
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Author : Vadim Olshevsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Structured Matrices In Mathematics Computer Science And Engineering I written by Vadim Olshevsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Matrices categories.
"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.
Numerical Solution Of The Coupled Algebraic Riccati Equations
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Author : Prasanthan Rajasingam
language : en
Publisher:
Release Date : 2013
Numerical Solution Of The Coupled Algebraic Riccati Equations written by Prasanthan Rajasingam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
In this paper we develop new and improved results in the numerical solution of the coupled algebraic Riccati equations. First we provide improved matrix upper bounds on the positive semidefinite solution of the unified coupled algebraic Riccati equations. Our approach is largely inspired by recent results established by Liu and Zhang. Our main results tighten the estimates of the relevant dominant eigenvalues. Also by relaxing the key restriction our upper bound applies to a larger number of situations. We also present an iterative algorithm to refine the new upper bounds and the lower bounds and numerically compute the solutions of the unified coupled algebraic Riccati equations. This construction follows the approach of Gao, Xue and Sun but we use different bounds. This leads to different analysis on convergence. Besides, we provide new matrix upper bounds for the positive semidefinite solution of the continuous coupled algebraic Riccati equations. By using an alternative primary assumption we present a new upper bound. We follow the idea of Davies, Shi and Wiltshire for the non-coupled equation and extend their results to the coupled case. We also present an iterative algorithm to improve our upper bounds. Finally we improve the classical Newton's method by the line search technique to compute the solutions of the continuous coupled algebraic Riccati equations. The Newton's method for couple Riccati equations is attributed to Salama and Gourishanar, but we construct the algorithm in a different way using the Frechet derivative and we include line search too. Our algorithm leads to a faster convergence compared with the classical scheme. Numerical evidence is also provided to illustrate the performance of our algorithm.
Structure Preserving Doubling Algorithms For Nonlinear Matrix Equations
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Author : Tsung-Ming Huang
language : en
Publisher: SIAM
Release Date : 2018-10-04
Structure Preserving Doubling Algorithms For Nonlinear Matrix Equations written by Tsung-Ming Huang and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Mathematics categories.
Nonlinear matrix equations arise frequently in applied science and engineering. This is the first book to provide a unified treatment of structure-preserving doubling algorithms that have been recently studied and proven effective for notoriously challenging problems, such as fluid queue theory and vibration analysis for high speed trains; present recent developments and results for the theory of doubling algorithms for nonlinear matrix equations associated with regular matrix pencils; and highlight the use of doubling algorithms in achieving robust solutions for notoriously challenging problems that other methods cannot. Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations is intended for researchers and computational scientists, and graduate students may also find it of interest.