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| Author | : Lloyd N. Trefethen |
| Publisher | : Princeton University Press |
| Total Pages | : |
| Release | : 2020-05-26 |
| Genre | : Mathematics |
| ISBN | : 0691213100 |
Download Spectra and Pseudospectra Book in PDF, ePub and Kindle
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 | : Lloyd N. Trefethen |
| Publisher | : Princeton University Press |
| Total Pages | : 634 |
| Release | : 2005-08-07 |
| Genre | : Mathematics |
| ISBN | : 9780691119465 |
Download Spectra and Pseudospectra Book in PDF, ePub and Kindle
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 | : E. Brian Davies |
| Publisher | : Cambridge University Press |
| Total Pages | : 436 |
| Release | : 2007-04-26 |
| Genre | : Mathematics |
| ISBN | : 1139464337 |
Download Linear Operators and their Spectra Book in PDF, ePub and Kindle
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 | : Albrecht Boettcher |
| Publisher | : SIAM |
| Total Pages | : 421 |
| Release | : 2005-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898717853 |
Download Spectral Properties of Banded Toeplitz Matrices Book in PDF, ePub and Kindle
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 |
| Total Pages | : 248 |
| Release | : 1998-10-28 |
| Genre | : Mathematics |
| ISBN | : 9780521645645 |
Download A Practical Guide to Pseudospectral Methods Book in PDF, ePub and Kindle
This book explains how, when and why the pseudospectral approach works.
| Author | : Aref Jeribi |
| Publisher | : CRC Press |
| Total Pages | : 208 |
| Release | : 2018-04-17 |
| Genre | : Mathematics |
| ISBN | : 135104625X |
Download Linear Operators and Their Essential Pseudospectra Book in PDF, ePub and Kindle
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 | : Lloyd N. Trefethen |
| Publisher | : SIAM |
| Total Pages | : 179 |
| Release | : 2000-07-01 |
| Genre | : Mathematics |
| ISBN | : 0898714656 |
Download Spectral Methods in MATLAB Book in PDF, ePub and Kindle
Mathematics of Computing -- Numerical Analysis.
| Author | : Maolin Che |
| Publisher | : Springer Nature |
| Total Pages | : 250 |
| Release | : 2020-04-01 |
| Genre | : Mathematics |
| ISBN | : 9811520593 |
Download Theory and Computation of Complex Tensors and its Applications Book in PDF, ePub and Kindle
The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.
| Author | : Lloyd Nicholas Trefethen |
| Publisher | : |
| Total Pages | : 46 |
| Release | : 1995 |
| Genre | : Eigenvalues |
| ISBN | : |
Download Pseudospectra of Linear Operators Book in PDF, ePub and Kindle
| Author | : Aref Jeribi |
| Publisher | : Springer |
| Total Pages | : 599 |
| Release | : 2015-07-04 |
| Genre | : Science |
| ISBN | : 3319175661 |
Download Spectral Theory and Applications of Linear Operators and Block Operator Matrices Book in PDF, ePub and Kindle
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.
