Infinite Matrices And Their Finite Sections
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Infinite Matrices And Their Finite Sections
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Author : Marko Lindner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-10
Infinite Matrices And Their Finite Sections written by Marko Lindner 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 2006-11-10 with Mathematics categories.
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.
Infinite Matrices And Their Recent Applications
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Author : P.N. Shivakumar
language : en
Publisher: Springer
Release Date : 2016-06-20
Infinite Matrices And Their Recent Applications written by P.N. Shivakumar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
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.
Toeplitz Matrices Asymptotic Linear Algebra And Functional Analysis
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Author : Albrecht Böttcher
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Toeplitz Matrices Asymptotic Linear Algebra And Functional Analysis written by Albrecht Böttcher 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 2000 with C*-algebras categories.
This text is a self-contained introduction to some problems for Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The text looks at Toeplitz matrices with rational symbols, and focuses attention on the asymptotic behavior of the singular values, which includes the behavior of the norms, the norms of the inverses, and the condition numbers as special cases. The text illustrates that the asymptotics of several linear algebra characteristics depend in a fascinating way on functional analytic properties of infinite matrices. Many convergence results can very comfortably be obtained by working with appropriate C*-algebras, while refinements of these results, for example, estimates of the convergence speed, nevertheless require hard analysis.
Toeplitz Matrices Asymptotic Linear Algebra And Functional Analysis
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Author : Albrecht Böttcher
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Toeplitz Matrices Asymptotic Linear Algebra And Functional Analysis written by Albrecht Böttcher and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The subject of this text is the relation between the properties of infinite Toeplitz matrices ao a_I a_2 al ao a_I a2 al ao and their large finite sections This is very big and even inexhaustible subject, and therefore we must limit ourselves to a few concrete problems here. We will focus our attention on singular values. The singular values of An are the eigenvalues of (A~An)I/2. The properties of the singular values of An for fixed n (or, as in so-called interlacing theorems, for some consecutive n) are studied in linear algebra. The problem of determining the singular values of An for large n (say n = 700) is a business of numerical linear algebra. The behavior of the singular 23 values of An for n --+ 00 (or, say, for n = 10 ) is a concern of asymptotic linear algebra. Finally, the investigation of the properties of the infinite matrix A is a task of functional analysis. To get an idea of what this text is about, we cite a few questions we will consider. Preface viii Question 1. Does the smallest singular value 81 (An) stay away from zero as n -t oo? Because this is the question whether the norms IIA;;111 are uniformly bounded for all sufficiently large n.
Infinite Matrices And Sequence Spaces
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Author : Richard G. Cooke
language : en
Publisher: Courier Corporation
Release Date : 2014-06-10
Infinite Matrices And Sequence Spaces written by Richard G. Cooke and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-10 with Mathematics categories.
Clear, correct summation of basic results on general behavior of infinite matrices features three introductory chapters leading to applications related to summability of divergent sequences and series. Nearly 200 examples. 1950 edition.
Some Finite And Infinite Matrices Their Computations And Applications
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Author : Chuanxiang Ji
language : en
Publisher:
Release Date : 1998
Some Finite And Infinite Matrices Their Computations And Applications written by Chuanxiang Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Operators Semigroups Algebras And Function Theory
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Author : Yemon Choi
language : en
Publisher: Springer Nature
Release Date : 2023-12-06
Operators Semigroups Algebras And Function Theory written by Yemon Choi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-06 with Mathematics categories.
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.
Limit Operators Collective Compactness And The Spectral Theory Of Infinite Matrices
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Author : Simon N. Chandler-Wilde
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Limit Operators Collective Compactness And The Spectral Theory Of Infinite Matrices written by Simon N. Chandler-Wilde 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 2011 with Mathematics categories.
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 $\infty$.
Introduction To Large Truncated Toeplitz Matrices
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Author : Albrecht Böttcher
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Large Truncated Toeplitz Matrices written by Albrecht Böttcher 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 Mathematics categories.
Applying functional analysis and operator theory to some concrete asymptotic problems of linear algebra, this book contains results on the stability of projection methods, deals with asymptotic inverses and Moore-Penrose inversion of large Toeplitz matrices, and embarks on the asymptotic behaviour of the norms of inverses, the pseudospectra, the singular values, and the eigenvalues of large Toeplitz matrices. The approach is heavily based on Banach algebra techniques and nicely demonstrates the usefulness of C*-algebras and local principles in numerical analysis, including classical topics as well as results and methods from the last few years. Though employing modern tools, the exposition is elementary and points out the mathematical background behind some interesting phenomena encountered with large Toeplitz matrices. Accessible to readers with basic knowledge in functional analysis, the book addresses graduates, teachers, and researchers and should be of interest to everyone who has to deal with infinite matrices (Toeplitz or not) and their large truncations.
Large Truncated Toeplitz Matrices Toeplitz Operators And Related Topics
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Author : Dario A. Bini
language : en
Publisher: Birkhäuser
Release Date : 2017-03-21
Large Truncated Toeplitz Matrices Toeplitz Operators And Related Topics written by Dario A. Bini and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-21 with Mathematics categories.
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.