Download or read book On Mesh Independence and Newton type Methods written by Owe Axelsson and published by . This book was released on 1992 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Equations and its Applications written by Ioannis K. Argyros and published by CRC Press. This book was released on 2012-06-05 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter co

Download or read book A Mesh independence Result for Semismooth Newton Methods written by Michael Hintermüller and published by . This book was released on 2003 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mesh Dependence in PDE Constrained Optimisation written by Tobias Schwedes and published by Springer. This book was released on 2017-07-07 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to PDE-constrained optimisation using finite elements and the adjoint approach. The practical impact of the mathematical insights presented here are demonstrated using the realistic scenario of the optimal placement of marine power turbines, thereby illustrating the real-world relevance of best-practice Hilbert space aware approaches to PDE-constrained optimisation problems. Many optimisation problems that arise in a real-world context are constrained by partial differential equations (PDEs). That is, the system whose configuration is to be optimised follows physical laws given by PDEs. This book describes general Hilbert space formulations of optimisation algorithms, thereby facilitating optimisations whose controls are functions of space. It demonstrates the importance of methods that respect the Hilbert space structure of the problem by analysing the mathematical drawbacks of failing to do so. The approaches considered are illustrated using the optimisation problem arising in tidal array layouts mentioned above. This book will be useful to readers from engineering, computer science, mathematics and physics backgrounds interested in PDE-constrained optimisation and their real-world applications.

Download or read book Efficient Methods for Solving Equations and Variational Inequalities written by Ioannis K. Argyros and published by Polimetrica s.a.s.. This book was released on 2009 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mesh Independent Convergence of the Modified Inexact Newton Method for a Second Order Nonlinear Problem written by and published by . This book was released on 2004 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.

Download or read book written by and published by World Scientific. This book was released on with total page 1131 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces written by Michael Ulbrich and published by SIAM. This book was released on 2011-01-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.

Download or read book Numerical Analysis and Its Applications written by Lubin Vulkov and published by Springer Science & Business Media. This book was released on 1997-02-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Workshop on Numerical Analysis and Its Applications, WNAA'96, held in Rousse, Bulgaria, in June 1996. The 57 revised full papers presented were carefully selected and reviewed for inclusion in the volume; also included are 14 invited presentations. All in all, the book offers a wealth of new results and methods of numerical analysis applicable in computational science, particularly in computational physics and chemistry. The volume reflects that the cooperation of computer scientists, mathematicians and scientists provides new numerical tools for computational scientists and, at the same time, stimulates numerical analysis.

Download or read book Convergence and Applications of Newton type Iterations written by Ioannis K. Argyros and published by Springer Science & Business Media. This book was released on 2008-06-12 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for an advanced course on numerical functional analysis.

Download or read book Finite Difference Methods Theory and Applications written by Ivan Dimov and published by Springer. This book was released on 2019-01-28 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.

Download or read book Computational Methods In Nonlinear Analysis Efficient Algorithms Fixed Point Theory And Applications written by Ioannis K Argyros and published by World Scientific. This book was released on 2013-07-11 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory.This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.

Download or read book Approximate Solution Of Operator Equations With Applications written by Ioannis K Argyros and published by World Scientific Publishing Company. This book was released on 2005-08-26 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Intelligent Numerical Methods Applications to Fractional Calculus written by George A. Anastassiou and published by Springer. This book was released on 2015-12-07 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

Download or read book Numerical Analysis and Its Applications written by and published by . This book was released on 1996 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in the Efficiency of Computational Methods and Applications written by Ioannis K. Argyros and published by World Scientific. This book was released on 2000 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable textbook creates a general framework for the study of optimal iterative procedures for problems that are solved approximately. Emphasis is given to the efficiency of numerical methods. For generality the setting is abstract, but the book presents many applications to practical problems, allowing the reader to take advantage of the most modern high speed calculating devices, and provides examples to illustrate concepts and major theorems. The examples are selected from astrophysics (radiative transfer and the kinetic theory of gases), mechanics (elasticity), economics (predator -- prey problems), the n-dimensional Euclidean space and other applied areas. The book will benefit not only senior undergraduates, graduates, graduate students and researchers in the field but also those who wish to obtain information about specific results or techniques that take into account the particular nature of the equation.

Download or read book Newton Methods written by Ioannis K. Argyros and published by Nova Publishers. This book was released on 2005 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment offers a contemporary and systematic development of the theory and application of Newton methods, which are undoubtedly the most effective tools for solving equations appearing in computational sciences. Its focal point resides in an exhaustive analysis of the convergence properties of several Newton variants used in connection to specific real life problems originated from astrophysics, engineering, mathematical economics and other applied areas. What distinguishes this book from others is the fact that the weak convergence conditions inaugurated here allow for a wider applicability of Newton methods; finer error bounds on the distances involved, and a more precise information on the location of the solution. These factors make this book ideal for researchers, practitioners and students.