Spectra And Pseudospectra

Author : Lloyd N. Trefethen,Mark Embree
Publisher : Princeton University Press
Page : 128 pages
File Size : 43,5 Mb
Release : 2020-05-26
Category : Mathematics
ISBN : 9780691213101

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Spectra and Pseudospectra by Lloyd N. Trefethen,Mark Embree Pdf

Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

Author : Aref Jeribi
Publisher : CRC Press
Page : 208 pages
File Size : 48,5 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9781351046251

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Linear Operators and Their Essential Pseudospectra by Aref Jeribi Pdf

Linear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.

Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 436 pages
File Size : 41,5 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9781139464338

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Linear Operators and their Spectra by E. Brian Davies Pdf

This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.

Author : Torge Schmidt
Publisher : Unknown
Page : 128 pages
File Size : 51,8 Mb
Release : 2017
Category : Electronic
ISBN : 3843931690

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Approximation of Spectra and Pseudospectra on a Hilbert Space by Torge Schmidt Pdf

Author : Albrecht Boettcher,Sergei M. Grudsky
Publisher : SIAM
Page : 421 pages
File Size : 51,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 089871785X

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Spectral Properties of Banded Toeplitz Matrices by Albrecht Boettcher,Sergei M. Grudsky Pdf

This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge. Covering everything from classic results to the most recent developments, Spectral Properties of Banded Toeplitz Matrices is an important resource. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers.

Author : Bengt Fornberg
Publisher : Cambridge University Press
Page : 248 pages
File Size : 49,8 Mb
Release : 1998-10-28
Category : Mathematics
ISBN : 0521645646

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A Practical Guide to Pseudospectral Methods by Bengt Fornberg Pdf

This book explains how, when and why the pseudospectral approach works.

Author : Aref Jeribi
Publisher : Springer
Page : 599 pages
File Size : 44,8 Mb
Release : 2015-07-04
Category : Science
ISBN : 9783319175669

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Spectral Theory and Applications of Linear Operators and Block Operator Matrices by Aref Jeribi Pdf

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 179 pages
File Size : 50,6 Mb
Release : 2000-07-01
Category : Mathematics
ISBN : 9780898714654

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Spectral Methods in MATLAB by Lloyd N. Trefethen Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Leslie Hogben
Publisher : CRC Press
Page : 1838 pages
File Size : 45,9 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781466507296

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Handbook of Linear Algebra by Leslie Hogben Pdf

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and

Author : Leonid Bunimovich,Benjamin Webb
Publisher : Springer
Page : 189 pages
File Size : 52,6 Mb
Release : 2014-09-03
Category : Mathematics
ISBN : 9781493913756

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Isospectral Transformations by Leonid Bunimovich,Benjamin Webb Pdf

This book presents a new approach to the analysis of networks, which emphasizes how one can compress a network while preserving all information relative to the network's spectrum. Besides these compression techniques, the authors introduce a number of other isospectral transformations and demonstrate how, together, these methods can be applied to gain new results in a number of areas. This includes the stability of time-delayed and non time-delayed dynamical networks, eigenvalue estimation, pseudospectra analysis and the estimation of survival probabilities in open dynamical systems. The theory of isospectral transformations, developed in this text, can be readily applied in any area that involves the analysis of multidimensional systems and is especially applicable to the analysis of network dynamics. This book will be of interest to Mathematicians, Physicists, Biologists, Engineers and to anyone who has an interest in the dynamics of networks.

Author : Mark Ainsworth,Jeremy Levesley,Marco Marletta
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662039724

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The Graduate Student’s Guide to Numerical Analysis ’98 by Mark Ainsworth,Jeremy Levesley,Marco Marletta Pdf

Detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics, with each set of notes presenting a self-contained guide to a current research area and supplemented by an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. They start from a level suitable for first year graduates in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. Readers will thus quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described, and directions for future research given.

Author : Efstratios Gallopoulos,Bernard Philippe,Ahmed H. Sameh
Publisher : Springer
Page : 489 pages
File Size : 50,5 Mb
Release : 2015-07-25
Category : Technology & Engineering
ISBN : 9789401771887

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Parallelism in Matrix Computations by Efstratios Gallopoulos,Bernard Philippe,Ahmed H. Sameh Pdf

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.

Author : Sergeĭ Konstantinovich Godunov
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 46,6 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 0821808885

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Modern Aspects of Linear Algebra by Sergeĭ Konstantinovich Godunov Pdf

This book discusses fundamental ideas of linear algebra. The author presents the spectral theory of nonselfadjoint matrix operators and matrix pencils in a finite dimensional Euclidean space. Statements of computational problems and brief descriptions of numerical algorithms, some of them nontraditional, are given. Proved in detail are classical problems that are not usually found in standard university courses. In particular, the material shows the role of delicate estimates for the resolvent of an operator and underscores the need for the study and use of such estimates in numerical analysis.

Author : Robert M. Corless,Nicolas Fillion
Publisher : Springer Science & Business Media
Page : 869 pages
File Size : 50,9 Mb
Release : 2013-12-12
Category : Mathematics
ISBN : 9781461484530

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A Graduate Introduction to Numerical Methods by Robert M. Corless,Nicolas Fillion Pdf

This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

Author : Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
Publisher : SIAM
Page : 710 pages
File Size : 54,9 Mb
Release : 2017-07-07
Category : Mathematics
ISBN : 9781611974898

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Foundations of Applied Mathematics, Volume I by Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans Pdf

This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?