Algebraic Methods for Toeplitz-like Matrices and Operators
Author: G. Heinig
Publisher: Birkhäuser
Published: 2013-11-21
Total Pages: 213
ISBN-13: 3034862415
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Algebraic methods for Toeplitz-like matrices and operators
Toeplitz Matrices and Singular Integral Equations
Author: Albrecht Böttcher
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 327
ISBN-13: 3034881991
DOWNLOAD EBOOK →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.
Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis
Author: Albrecht Böttcher
Publisher: Springer Science & Business Media
Published: 2000
Total Pages: 132
ISBN-13: 9783764362904
DOWNLOAD EBOOK →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 and Operators
Author: Nikolaï Nikolski
Publisher: Cambridge University Press
Published: 2020-01-02
Total Pages: 453
ISBN-13: 110719850X
DOWNLOAD EBOOK →A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.
Numerical Methods for Structured Matrices and Applications
Author: Dario Andrea Bini
Publisher: Springer Science & Business Media
Published: 2011-02-09
Total Pages: 439
ISBN-13: 3764389966
DOWNLOAD EBOOK →This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.
Toeplitz Matrices and Operators
Author: Nikolaï Nikolski
Publisher: Cambridge University Press
Published: 2020-01-02
Total Pages: 453
ISBN-13: 1108187579
DOWNLOAD EBOOK →The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others. This friendly introduction to Toeplitz theory covers the classical spectral theory of Toeplitz forms and Wiener–Hopf integral operators and their manifestations throughout modern functional analysis. Numerous solved exercises illustrate the results of the main text and introduce subsidiary topics, including recent developments. Each chapter ends with a survey of the present state of the theory, making this a valuable work for the beginning graduate student and established researcher alike. With biographies of the principal creators of the theory and historical context also woven into the text, this book is a complete source on Toeplitz theory.
Toeplitz Operators and Random Matrices
Author: Estelle Basor
Publisher: Springer Nature
Published: 2023-01-01
Total Pages: 606
ISBN-13: 3031138511
DOWNLOAD EBOOK →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.
Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications
Author: Daniele Bertaccini
Publisher: CRC Press
Published: 2018-02-19
Total Pages: 375
ISBN-13: 1498764177
DOWNLOAD EBOOK →This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Matrix Computations and Semiseparable Matrices
Author: Raf Vandebril
Publisher: JHU Press
Published: 2008-01-14
Total Pages: 594
ISBN-13: 0801896797
DOWNLOAD EBOOK →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.
