Infinite Matrices And Their Finite Sections
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| Author | : Marko Lindner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 203 |
| Release | : 2006-11-10 |
| Genre | : Mathematics |
| ISBN | : 3764377674 |
Download Infinite Matrices and their Finite Sections Book in PDF, Epub and Kindle
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 |
| Total Pages | : 124 |
| Release | : 2016-06-20 |
| Genre | : Mathematics |
| ISBN | : 3319301802 |
Download Infinite Matrices and Their Recent Applications Book in PDF, Epub and Kindle
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 | : Albrecht Böttcher |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 132 |
| Release | : 2000 |
| Genre | : C*-algebras |
| ISBN | : 9783764362904 |
Download Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis Book in PDF, Epub and Kindle
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.
| Author | : Yemon Choi |
| Publisher | : Springer Nature |
| Total Pages | : 262 |
| Release | : 2023-12-06 |
| Genre | : Mathematics |
| ISBN | : 3031380207 |
Download Operators, Semigroups, Algebras and Function Theory Book in PDF, Epub and Kindle
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. |
| Total Pages | : 126 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821852434 |
Download Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices Book in PDF, Epub and Kindle
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 |
| Total Pages | : 757 |
| Release | : 2017-03-21 |
| Genre | : Mathematics |
| ISBN | : 3319491822 |
Download Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics Book in PDF, Epub and Kindle
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 | : Albrecht Böttcher |
| Publisher | : Birkhäuser |
| Total Pages | : 112 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9783034883955 |
Download Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis Book in PDF, Epub and Kindle
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.
| Author | : Michiel Hazewinkel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 543 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401512337 |
Download Encyclopaedia of Mathematics Book in PDF, Epub and Kindle
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 |
| Total Pages | : 413 |
| Release | : 2017-01-24 |
| Genre | : Mathematics |
| ISBN | : 3319498878 |
Download Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications Book in PDF, Epub and Kindle
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. |
| Total Pages | : 282 |
| Release | : 2016-08-25 |
| Genre | : Mathematics |
| ISBN | : 1470419289 |
Download Topics in Functional Analysis and Algebra Book in PDF, Epub and Kindle
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.
