Author: Nikolaĭ Stepanovich Kurpelʹ
Publisher: American Mathematical Soc.
ISBN: 9780821815960
Category : Mathematics
Languages : en
Pages : 204

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Author: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537

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Mathematics of Computing -- General.

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: N. S. Kurpel'
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: W.M., III. Patterson
Publisher: Springer
ISBN: 3540384553
Category : Mathematics
Languages : en
Pages : 187

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In this expository work we shall conduct a survey of iterative techniques for solving the linear operator equations Ax=y in a Hilbert space. Whenever convenient these iterative schemes are given in the context of a complex Hilbert space -- Chapter II is devoted to those methods (three in all) which are given only for real Hilbert space. Thus chapter III covers those methods which are valid in a complex Hilbert space except for the two methods which are singled out for special attention in the last two chapters. Specifically, the method of successive approximations is covered in Chapter IV, and Chapter V consists of a discussion of gradient methods. While examining these techniques, our primary concern will be with the convergence of the sequence of approximate solutions. However, we shall often look at estimates of the error and the speed of convergence of a method.

Author: Nikolai S. Kurpel'
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: A.B. Bakushinsky
Publisher: Springer Science & Business Media
ISBN: 140203122X
Category : Mathematics
Languages : en
Pages : 298

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This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.

Author: Otmar Scherzer
Publisher: Springer Science & Business Media
ISBN: 0387929193
Category : Mathematics
Languages : en
Pages : 1626

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Book Description
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.

Author: Ioannis K Argyros
Publisher: World Scientific Publishing Company
ISBN: 9813106549
Category : Mathematics
Languages : en
Pages : 527

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Book Description
Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.

Author: Charles L. Byrne
Publisher: A K Peters/CRC Press
ISBN:
Category : Mathematics
Languages : en
Pages : 408

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Book Description
This book is a collection of essays on iterative algorithms and their uses. It focuses on the mathematics of medical image reconstruction, with emphasis on Fourier inversion. The book discusses the problems and algorithms in the context of operators on finite-dimensional Euclidean space.