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Author: Marko Lindner
Publisher: Springer Science & Business Media
ISBN: 3764377674
Category : Mathematics
Languages : en
Pages : 203
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Book Description
This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering.
Author: Marko Lindner
Publisher: Springer Science & Business Media
ISBN: 3764377674
Category : Mathematics
Languages : en
Pages : 203
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Book Description
This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering.
Author: P.N. Shivakumar
Publisher: Springer
ISBN: 3319301802
Category : Mathematics
Languages : en
Pages : 124
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Book Description
This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such as Bessel’s and Mathieu’s equations, viscous fluid flow in doubly connected regions, digital circuit dynamics and eigenvalues of the Laplacian.
Author: Yemon Choi
Publisher: Springer Nature
ISBN: 3031380207
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.
Author: Simon N. Chandler-Wilde
Publisher: American Mathematical Soc.
ISBN: 0821852434
Category : Mathematics
Languages : en
Pages : 126
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Book Description
In the first half of this memoir the authors explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). They build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator $A$ (its operator spectrum). In the second half of this memoir the authors study bounded linear operators on the generalised sequence space $\ell^p(\mathbb{Z}^N,U)$, where $p\in [1,\infty]$ and $U$ is some complex Banach space. They make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator $A$ is a locally compact perturbation of the identity. Especially, they obtain stronger results than previously known for the subtle limiting cases of $p=1$ and $\infty$.
Author: Dario A. Bini
Publisher: Birkhäuser
ISBN: 3319491822
Category : Mathematics
Languages : en
Pages : 757
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Book Description
This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Böttcher’s 60th birthday. Albrecht Böttcher himself has made substantial contributions to the subject in the past. The book also includes a biographical essay, a complete bibliography of Albrecht Böttcher’s work and brief informal notes on personal encounters with him. The book is of interest to graduate and advanced undergraduate students majoring in mathematics, researchers in matrix and operator theory as well as engineers and applied mathematicians.
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9401512337
Category : Mathematics
Languages : en
Pages : 543
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Book Description
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author: Michele Benzi
Publisher: Springer
ISBN: 3319498878
Category : Mathematics
Languages : en
Pages : 413
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Book Description
Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Author: Bernard Russo
Publisher: American Mathematical Soc.
ISBN: 1470419289
Category : Mathematics
Languages : en
Pages : 282
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Book Description
The USA-Uzbekistan Conference on Analysis and Mathematical Physics, focusing on contemporary issues in dynamical systems, mathematical physics, operator algebras, and several complex variables, was hosted by California State University, Fullerton, from May 20–23, 2014. The main objective of the conference was to facilitate scientific communication and collaboration between mathematicians from the USA and Uzbekistan. This volume contains the proceedings of the Special Session on Algebra and Functional Analysis. The theory of operator algebras is the unified theme for many papers in this volume. Out of four extensive survey papers, two cover problems related to derivation of various algebras of functions. The other two surveys are on classification of Leibniz algebras and on evolution algebras. The sixteen research articles are devoted to certain analytic topics, such as minimal projections with respect to numerical radius, functional equations and discontinuous polynomials, Fourier inversion for distributions, Schrödinger operators, convexity and dynamical systems.
Author: Lakhmi C. Jain
Publisher: Springer Nature
ISBN: 9811526001
Category : Technology & Engineering
Languages : en
Pages : 386
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Book Description
This book discusses physical and mathematical models, numerical methods, computational algorithms and software complexes, which allow high-precision mathematical modeling in fluid, gas, and plasma mechanics; general mechanics; deformable solid mechanics; and strength, destruction and safety of structures. These proceedings focus on smart technologies and software systems that provide effective solutions to real-world problems in applied mechanics at various multi-scale levels. Highlighting the training of specialists for the aviation and space industry, it is a valuable resource for experts in the field of applied mathematics and mechanics, mathematical modeling and information technologies, as well as developers of smart applied software systems.
Author: Albrecht Boettcher
Publisher: SIAM
ISBN: 0898715997
Category : Mathematics
Languages : en
Pages : 410
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Book Description
“This is a wonderful book, full of the latest material on Toeplitz matrices and operators, including norms, spectra, pseudospectra, fields of values, and polynomial hulls. The notes at the end of the chapters are especially interesting and the exercises are challenging. The writing is careful and precise but also entertaining.” --Anne Greenbaum, Professor of Mathematics, University of Washington.“This book is a tremendous resource for all aspects of the spectral theory of banded Toeplitz matrices. It will be the first place I turn when looking for many results in this field, and given this book's amazing breadth and depth, I expect to find just what I need.” -- Mark Embree, Assistant Professor of Computational and Applied Mathematics, Rice University.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. The book may serve both as a text for introducing the material and as a reference. The approach is based on the know-how and experience of the authors in combining functional analytical methods with hard analysis and in applying operator theoretical methods to matrix theory, which reveals the essence of several phenomena and leads to significant improvements in existing results. All basic results presented in the book are precisely stated as theorems and accompanied by full proofs.Audience This book is written for applied mathematicians, engineers, and scientists who encounter Toeplitz matrices in their research. It also will be of interest to mathematicians in the fields of operator theory, numerical analysis, structured matrices, or random matrix theory, and physicists, chemists, biologists, and economists who deal with stationary statistical and stochastic problems. Parts of the book are suitable for use as a graduate-level text on Toeplitz matrices or analysis.Contents Preface; Chapter 1: Infinite Matrices; Chapter 2: Determinants; Chapter 3: Stability; Chapter 4: Instability; Chapter 5: Norms; Chapter 6: Condition Numbers; Chapter 7: Substitutes for the Spectrum; Chapter 8: Transient Behavior; Chapter 9: Singular Values; Chapter 10: Extreme Eigenvalues; Chapter 11: Eigenvalue Distribution; Chapter 12: Eigenvectors and Pseudomodes; Chapter 13: Structured Perturbations; Chapter 14: Impurities; Bibliography; Index.
