Download or read book Toeplitz Matrices and Operators written by Nikolaï Nikolski and published by Cambridge University Press. This book was released on 2020-01-02 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.
Download or read book Toeplitz Matrices Asymptotic Linear Algebra and Functional Analysis written by Albrecht Böttcher and published by Springer Science & Business Media. This book was released on 2000 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Large Truncated Toeplitz Matrices written by Albrecht Böttcher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Toeplitz and Circulant Matrices written by Robert M. Gray and published by Now Publishers Inc. This book was released on 2006 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.
Download or read book Spectral Properties of Banded Toeplitz Matrices written by Albrecht Boettcher and published by SIAM. This book was released on 2005-01-01 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Toeplitz Matrices and Singular Integral Equations written by Albrecht Böttcher and published by Birkhäuser. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.
Download or read book The Absolute Continuity of Toeplitz s Matrices written by Marvin Rosenblum and published by . This book was released on 1959 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Large Truncated Toeplitz Matrices Toeplitz Operators and Related Topics written by Dario A. Bini and published by Birkhäuser. This book was released on 2017-03-21 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Iterative Toeplitz Solvers written by Raymond Hon-Fu Chan and published by SIAM. This book was released on 2007-01-01 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Toeplitz systems arise in a variety of applications in mathematics, scientific computing, and engineering, including numerical partial and ordinary differential equations, numerical solutions of convolution-type integral equations, stationary autoregressive time series in statistics, minimal realization problems in control theory, system identification problems in signal processing, and image restoration problems in image processing.
Download or read book Toeplitz Operators and Random Matrices written by Estelle Basor and published by Springer Nature. This book was released on 2023-01-01 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.
Download or read book Toeplitz Forms and Their Applications written by Ulf Grenander and published by Univ of California Press. This book was released on with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hankel and Toeplitz Matrices and Forms written by Iosif Semenovich Iokhvidov and published by . This book was released on 1982 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summary: the story of the love affairs of John Reed & Louise Bryant in a war-torn world and how the Russian Revolution shook their lives.
Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril and published by JHU Press. This book was released on 2007-12-18 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
Download or read book Analysis of Toeplitz Operators written by Albrecht Böttcher and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised introduction to the advanced analysis of block Toeplitz operators including recent research. This book builds on the success of the first edition which has been used as a standard reference for fifteen years. Topics range from the analysis of locally sectorial matrix functions to Toeplitz and Wiener-Hopf determinants. This will appeal to both graduate students and specialists in the theory of Toeplitz operators.
Download or read book Matrix Analysis written by Roger A. Horn and published by Cambridge University Press. This book was released on 2012-10-22 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.
Download or read book Algebraic Methods for Toeplitz like Matrices and Operators written by G. Heinig and published by Birkhäuser. This book was released on 2013-11-21 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structured Matrices in Numerical Linear Algebra written by Dario Andrea Bini and published by Springer. This book was released on 2019-04-08 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.
