Iterative Methods for Toeplitz Systems PDF Download
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Author: Michael K. Ng
Publisher: Numerical Mathematics and Scie
ISBN: 9780198504207
Category : Computers
Languages : en
Pages : 370
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Book Description
Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing.
Author: Michael K. Ng
Publisher: Numerical Mathematics and Scie
ISBN: 9780198504207
Category : Computers
Languages : en
Pages : 370
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Book Description
Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing.
Author: Raymond Hon-Fu Chan
Publisher: SIAM
ISBN: 9780898718850
Category : Mathematics
Languages : en
Pages : 123
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Book Description
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.
Author: Xiao-Qing Jin
Publisher: Springer Science & Business Media
ISBN: 9781402008306
Category : Computers
Languages : en
Pages : 236
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Book Description
This volume contains the latest developments in the use of iterative methods to block Toeplitz systems. These systems arise in a variety of applications in mathematics, scientific computing, and engineering, such as image processing, numerical differential equations and integral equations, time series analysis, and control theory. Iterative methods such as Krylov subspace methods and multigrid methods are proposed to solve block Toeplitz systems. One of the main advantages of these iterative methods is that the operation cost of solving a large class of mn × mn block Toeplitz systems only requires O (mn log mn) operations. This book is the first book on Toeplitz iterative solvers and it includes recent research results. The author belongs to one of the most important groups in the field of structured matrix computation. The book is accessible to readers with a working knowledge of numerical linear algebra. It should be of interest to everyone who deals with block Toeplitz systems, numerical linear algebra, partial differential equations, ordinary differential equations, image processing, and approximation theory.
Author: Maxim A. Olshanskii
Publisher: SIAM
ISBN: 1611973465
Category : Mathematics
Languages : en
Pages : 257
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Book Description
Iterative Methods for Linear Systems?offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.??
Author: Daniele Bertaccini
Publisher: CRC Press
ISBN: 1351649612
Category : Mathematics
Languages : en
Pages : 366
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Book Description
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.
Author: David R. Kincaid
Publisher: Academic Press
ISBN: 1483260208
Category : Mathematics
Languages : en
Pages : 350
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Book Description
Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.
Author: Owe Axelsson
Publisher: Cambridge University Press
ISBN: 9780521555692
Category : Mathematics
Languages : en
Pages : 676
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Book Description
This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.
Author: George Em Karniadakis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110571684
Category : Mathematics
Languages : en
Pages : 360
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Book Description
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.
Author: Juan R. Torregrosa
Publisher: MDPI
ISBN: 3039219405
Category : Mathematics
Languages : en
Pages : 494
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Book Description
Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
Author: Raymond Chan
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 400
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Book Description
Because of the rapid evolution of the development of this field, as well as the fact that iterative methods are not often developed in a generic form for general applications, there is a lack of published materials that treat the topic properly and fully. These lectures from the Winter School on Iterative Methods in Scientific Computing and their Applications aims to bridge such a gap in the literature.
