Toeplitz And Circulant Matrices

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Toeplitz and Circulant Matrices

Author : Robert M. Gray
Publisher : Now Publishers Inc
ISBN 13 : 1933019239
Total Pages : 105 pages
Book Rating : 4.9/5 (33 download)

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Book Synopsis Toeplitz and Circulant Matrices by : Robert M. Gray

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.

Toeplitz and Circulant Matrices

Author : Robert M. Gray
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.:/5 (836 download)

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Book Synopsis Toeplitz and Circulant Matrices by : Robert M. Gray

Download or read book Toeplitz and Circulant Matrices written by Robert M. Gray and published by . This book was released on 1977 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Properties of Banded Toeplitz Matrices

Author : Albrecht Boettcher
Publisher : SIAM
ISBN 13 : 9780898717853
Total Pages : 421 pages
Book Rating : 4.7/5 (178 download)

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Book Synopsis Spectral Properties of Banded Toeplitz Matrices by : Albrecht Boettcher

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.

Introduction to Large Truncated Toeplitz Matrices

Author : Albrecht Böttcher
Publisher : Springer Science & Business Media
ISBN 13 : 1461214262
Total Pages : 264 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Large Truncated Toeplitz Matrices by : Albrecht Böttcher

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.

Bounds for the Eigenvalues of a Matrix

Author : Kenneth R. Garren
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Bounds for the Eigenvalues of a Matrix by : Kenneth R. Garren

Download or read book Bounds for the Eigenvalues of a Matrix written by Kenneth R. Garren and published by . This book was released on 1968 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Circulant Matrices

Author : Philip J. Davis
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Circulant Matrices by : Philip J. Davis

Download or read book Circulant Matrices written by Philip J. Davis and published by John Wiley & Sons. This book was released on 1979 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Iterative Toeplitz Solvers

Author : Raymond Hon-Fu Chan
Publisher : SIAM
ISBN 13 : 9780898718850
Total Pages : 123 pages
Book Rating : 4.7/5 (188 download)

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Book Synopsis An Introduction to Iterative Toeplitz Solvers by : Raymond Hon-Fu Chan

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.

Iterative Methods for Toeplitz Systems

Author : Michael K. Ng
Publisher : Numerical Mathematics and Scie
ISBN 13 : 9780198504207
Total Pages : 370 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Iterative Methods for Toeplitz Systems by : Michael K. Ng

Download or read book Iterative Methods for Toeplitz Systems written by Michael K. Ng and published by Numerical Mathematics and Scie. This book was released on 2004 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing.

Toeplitz Forms and Their Applications

Author : Ulf Grenander
Publisher : Univ of California Press
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4./5 ( download)

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Book Synopsis Toeplitz Forms and Their Applications by : Ulf Grenander

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:

Linear Algebra Via Exterior Products

Author : Sergei Winitzki
Publisher : Sergei Winitzki
ISBN 13 : 140929496X
Total Pages : 286 pages
Book Rating : 4.4/5 (92 download)

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Book Synopsis Linear Algebra Via Exterior Products by : Sergei Winitzki

Download or read book Linear Algebra Via Exterior Products written by Sergei Winitzki and published by Sergei Winitzki. This book was released on 2009-07-30 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.

Random Matrices and Non-Commutative Probability

Author : Arup Bose
Publisher : CRC Press
ISBN 13 : 1000458822
Total Pages : 420 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Random Matrices and Non-Commutative Probability by : Arup Bose

Download or read book Random Matrices and Non-Commutative Probability written by Arup Bose and published by CRC Press. This book was released on 2021-10-26 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.

Patterned Random Matrices

Author : Arup Bose
Publisher : CRC Press
ISBN 13 : 0429948891
Total Pages : 269 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Patterned Random Matrices by : Arup Bose

Download or read book Patterned Random Matrices written by Arup Bose and published by CRC Press. This book was released on 2018-05-23 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications. This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the March enko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices. Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.

Singular Value Computations for Toeplitz Matrices and Subspace Tracking

Author : Eva Lundström
Publisher :
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Singular Value Computations for Toeplitz Matrices and Subspace Tracking by : Eva Lundström

Download or read book Singular Value Computations for Toeplitz Matrices and Subspace Tracking written by Eva Lundström and published by . This book was released on 1998 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Random Circulant Matrices

Author : Arup Bose
Publisher : CRC Press
ISBN 13 : 0429788185
Total Pages : 152 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Random Circulant Matrices by : Arup Bose

Download or read book Random Circulant Matrices written by Arup Bose and published by CRC Press. This book was released on 2018-11-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.

Pell and Pell–Lucas Numbers with Applications

Author : Thomas Koshy
Publisher : Springer
ISBN 13 : 1461484898
Total Pages : 444 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Pell and Pell–Lucas Numbers with Applications by : Thomas Koshy

Download or read book Pell and Pell–Lucas Numbers with Applications written by Thomas Koshy and published by Springer. This book was released on 2014-11-11 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences. A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book. Finally, Pell and Pell–Lucas Numbers provides enjoyment and excitement while sharpening the reader’s mathematical skills involving pattern recognition, proof-and-problem-solving techniques.

Spectra and Pseudospectra

Author : Lloyd N. Trefethen
Publisher : Princeton University Press
ISBN 13 : 9780691119465
Total Pages : 634 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Spectra and Pseudospectra by : Lloyd N. Trefethen

Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen and published by Princeton University Press. This book was released on 2005-08-07 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics

Author : Dario A. Bini
Publisher : Birkhäuser
ISBN 13 : 3319491822
Total Pages : 757 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics by : Dario A. Bini

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.