Handbook of Mathematical Methods in Imaging

Handbook of Mathematical Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 1626
Release: 2010-11-23
Genre: Mathematics
ISBN: 0387929193

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

An Introduction to Iterative Toeplitz Solvers

An Introduction to Iterative Toeplitz Solvers
Author: Raymond Hon-Fu Chan
Publisher: SIAM
Total Pages: 123
Release: 2007-01-01
Genre: Mathematics
ISBN: 9780898718850

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 Solving Nonlinear Equations and Systems

Iterative Methods for Solving Nonlinear Equations and Systems
Author: Juan R. Torregrosa
Publisher: MDPI
Total Pages: 494
Release: 2019-12-06
Genre: Mathematics
ISBN: 3039219405

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.

Computational Methods for Inverse Problems

Computational Methods for Inverse Problems
Author: Curtis R. Vogel
Publisher: SIAM
Total Pages: 195
Release: 2002-01-01
Genre: Mathematics
ISBN: 0898717574

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications

Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications
Author: Daniele Bertaccini
Publisher: CRC Press
Total Pages: 321
Release: 2018-02-19
Genre: Mathematics
ISBN: 1351649612

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.

The Variational Approach to Fracture

The Variational Approach to Fracture
Author: Blaise Bourdin
Publisher: Springer Science & Business Media
Total Pages: 173
Release: 2008-04-19
Genre: Technology & Engineering
ISBN: 1402063954

Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.

Iterative Solution of Large Linear Systems

Iterative Solution of Large Linear Systems
Author: David M. Young
Publisher: Elsevier
Total Pages: 599
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483274136

Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.