Numerical Methods for General and Structured Eigenvalue Problems
Numerical Methods for General and Structured Eigenvalue Problems

Author: Daniel Kressner

Publisher: Springer Science & Business Media

Published: 2006-01-20

Total Pages: 272

ISBN-13: 3540285024

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This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.

Numerical Methods for Large Eigenvalue Problems
Numerical Methods for Large Eigenvalue Problems

Author: Yousef Saad

Publisher: SIAM

Published: 2011-01-01

Total Pages: 292

ISBN-13: 9781611970739

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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Numerical Algorithms
Numerical Algorithms

Author: Justin Solomon

Publisher: CRC Press

Published: 2015-06-24

Total Pages: 400

ISBN-13: 1482251892

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Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

The Matrix Eigenvalue Problem
The Matrix Eigenvalue Problem

Author: David S. Watkins

Publisher: SIAM

Published: 2007-01-01

Total Pages: 452

ISBN-13: 9780898717808

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The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.

Proceedings of the Conference on Applied Mathematics and Scientific Computing
Proceedings of the Conference on Applied Mathematics and Scientific Computing

Author: Zlatko Drmac

Publisher: Springer Science & Business Media

Published: 2005-02-23

Total Pages: 362

ISBN-13: 9781402031960

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The Third Conference on Applied Mathematics and Scienti?c Computing took place June 23-27, 2003 on island of Brijuni, Croatia. The main goal of the conference was to interchange ideas among applied mathematicians in the broadest sense both from and outside academia, as well as experts from other areas who apply different mathematical techniques. During the meeting there were invited and contributed talksand software presentations. Invited presentations were given by active researchers from the ?eldsof approximation theory, numerical methods for differential equations and numericallinear algebra. These proceedings contain research and review papers by invited speakers and selected contributed papers from the ?elds of applied and numerical mathematics. A particular aim of the conference was to encourage young scientists to present results of their research. Traditionally, the best presentation given by PhD student was rewarded. This year awardee was Luka Grubisi ? c ́ (University of Hagen, Hagen, Germany) and we congratulate him for this achievement. It would be hard to organize the conference without generous support of the Croatian Ministry of Science and Technology and we acknowledge it. We are also indebted to themainorganizer, Department of Mathematics, University of Zagreb.Motivating beautiful nature should bealso mentioned.And, attheend, we are thankful to Drs. JosipTambaca ? and Ivica Nakic ́ for giving this book its ?nal shape.

Numerical Continuation Methods
Numerical Continuation Methods

Author: Eugene L. Allgower

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 402

ISBN-13: 3642612571

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Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.

Large Scale Eigenvalue Problems
Large Scale Eigenvalue Problems

Author: J. Cullum

Publisher: Elsevier

Published: 1986-01-01

Total Pages: 339

ISBN-13: 0080872387

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Results of research into large scale eigenvalue problems are presented in this volume. The papers fall into four principal categories:novel algorithms for solving large eigenvalue problems, novel computer architectures, computationally-relevant theoretical analyses, and problems where large scale eigenelement computations have provided new insight.

Eigenvalue Problems in Power Systems
Eigenvalue Problems in Power Systems

Author: Federico Milano

Publisher: CRC Press

Published: 2020-12-22

Total Pages: 407

ISBN-13: 1000335208

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The book provides a comprehensive taxonomy of non-symmetrical eigenvalues problems as applied to power systems. The book bases all formulations on mathematical concept of “matrix pencils” (MPs) and considers both regular and singular MPs for the eigenvalue problems. Each eigenvalue problem is illustrated with a variety of examples based on electrical circuits and/or power system models and controllers and related data are provided in the appendices of the book. Numerical methods for the solution of all considered eigenvalue problems are discussed. The focus is on large scale problems and, hence, attention is dedicated to the performance and scalability of the methods. The target of the book are researchers and graduated students in Electrical & Computer Science Engineering, both taught and research Master programmes as well as PhD programmes and it: explains eigenvalue problems applied into electrical power systems explains numerical examples on applying the mathematical methods, into studying small signal stability problems of realistic and large electrical power systems includes detailed and in-depth analysis including non-linear and other advanced aspects provides theoretical understanding and advanced numerical techniques essential for secure operation of power systems provides a comprehensive set of illustrative examples that support theoretical discussions

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

Author: Peter Benner

Publisher: Springer

Published: 2015-05-09

Total Pages: 635

ISBN-13: 3319152602

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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.