Toeplitz And Circulant Matrices
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Toeplitz And Circulant Matrices
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Author : Robert M. Gray
language : en
Publisher: Now Publishers Inc
Release Date : 2006
Toeplitz And Circulant Matrices written by Robert M. Gray and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
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
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Author : Robert M. Gray
language : en
Publisher:
Release Date : 1977
Toeplitz And Circulant Matrices written by Robert M. Gray and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Circulant Matrices
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Author : Philip J. Davis
language : en
Publisher: John Wiley & Sons
Release Date : 1979
Circulant Matrices written by Philip J. Davis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Spectral Properties Of Banded Toeplitz Matrices
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Author : Albrecht Boettcher
language : en
Publisher: SIAM
Release Date : 2005-01-01
Spectral Properties Of Banded Toeplitz Matrices written by Albrecht Boettcher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
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.
Random Circulant Matrices
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Author : Arup Bose
language : en
Publisher: CRC Press
Release Date : 2018-11-05
Random Circulant Matrices written by Arup Bose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
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.
Iterative Methods For Toeplitz Systems
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Author : Michael K. Ng
language : en
Publisher: Numerical Mathematics and Scie
Release Date : 2004
Iterative Methods For Toeplitz Systems written by Michael K. Ng and has been published by Numerical Mathematics and Scie this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing.
An Introduction To Iterative Toeplitz Solvers
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Author : Raymond Hon-Fu Chan
language : en
Publisher: SIAM
Release Date : 2007-01-01
An Introduction To Iterative Toeplitz Solvers written by Raymond Hon-Fu Chan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
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.
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.
Block Toeplitz Matrices
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Author : Jes S. Guti Rrez-Guti Rrez
language : en
Publisher: Now Pub
Release Date : 2012
Block Toeplitz Matrices written by Jes S. Guti Rrez-Guti Rrez and has been published by Now Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
Block Toeplitz Matrices: Asymptotic Results and Applications provides a tutorial introduction and in-depth expose of this important mathematical technique used in Communications, Information Theory, and Signal Processing. The matrix representations of discrete-time causal finite impulse response (FIR), multiple-input multiple-output (MIMO) filters, and correlation matrices of vector wide sense stationary (WSS) processes are all block Toeplitz. The monograph deals with the asymptotic behaviour of eigenvalues, products and inverses of block Toeplitz matrices, with the concept of asymptotically equivalent sequences of matrices being the key concept. However, since the blocks of block Toeplitz matrices are, in general, not square, the definition of asymptotically equivalent sequences of matrices are extended to sequences of non-square matrices. Furthermore, the monograph covers any function of block Toeplitz matrices and considers block Toeplitz matrices generated by the Fourier coefficients of any continuous matrix-valued function. Block Toeplitz Matrices is an advanced level tutorial on a mathematical technique with applications in many engineering disciplines.
Special Matrices Of Mathematical Physics
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Author : Ruben Aldrovandi
language : en
Publisher: World Scientific
Release Date : 2001
Special Matrices Of Mathematical Physics written by Ruben Aldrovandi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas concerning Lie algebra invariants, differential geometry and real gases, and their matrices are instrumental in the study of chaotic mappings.