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Symmetry with Operator Theory and Equations

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ISBN: 9783039216666 9783039216673 Year: Pages: 208 DOI: 10.3390/books978-3-03921-667-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data. This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.

Iterative Methods for Solving Nonlinear Equations and Systems

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ISBN: 9783039219407 9783039219414 Year: Pages: 494 DOI: 10.3390/books978-3-03921-941-4 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-01-07 09:08:26
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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.

Keywords

point projection --- intersection --- parametric curve --- n-dimensional Euclidean space --- Newton’s second order method --- fixed point theorem --- nonlinear equations --- multiple zeros --- optimal iterative methods --- higher order of convergence --- nonlinear operator equation --- Fréchet derivative --- ?-continuity condition --- Newton-like method --- Frédholm integral equation --- nonlinear equations --- Padé approximation --- iterative method --- order of convergence --- numerical experiment --- fourth order iterative methods --- local convergence --- banach space --- radius of convergence --- nonlinear equation --- iterative process --- non-differentiable operator --- Lipschitz condition --- high order --- sixteenth order convergence method --- local convergence --- dynamics --- Banach space --- Newton’s method --- semi-local convergence --- Kantorovich hypothesis --- iterative methods --- Steffensen’s method --- R-order --- with memory --- computational efficiency --- non-linear equation --- basins of attraction --- optimal order --- higher order method --- computational order of convergence --- nonlinear equations --- multiple roots --- Chebyshev–Halley-type --- optimal iterative methods --- efficiency index --- Banach space --- semilocal convergence --- ?-continuity condition --- Jarratt method --- error bound --- Fredholm integral equation --- Newton’s method --- global convergence --- variational inequality problem --- split variational inclusion problem --- multi-valued quasi-nonexpasive mappings --- Hilbert space --- sixteenth-order optimal convergence --- multiple-root finder --- asymptotic error constant --- weight function --- purely imaginary extraneous fixed point --- attractor basin --- drazin inverse --- generalized inverse --- iterative methods --- higher order --- efficiency index --- integral equation --- efficiency index --- nonlinear models --- iterative methods --- higher order --- nonlinear equations --- optimal iterative methods --- multiple roots --- efficiency index --- iterative methods --- nonlinear equations --- Newton-type methods --- smooth and nonsmooth operators --- heston model --- Hull–White --- option pricing --- PDE --- finite difference (FD) --- iteration scheme --- Moore–Penrose --- rectangular matrices --- rate of convergence --- efficiency index --- nonlinear equations --- conjugate gradient method --- projection method --- convex constraints --- signal and image processing --- nonlinear monotone equations --- conjugate gradient method --- projection method --- signal processing --- nonlinear systems --- multipoint iterative methods --- divided difference operator --- order of convergence --- Newton’s method --- computational efficiency index --- system of nonlinear equations --- Newton method --- Newton-HSS method --- nonlinear HSS-like method --- Picard-HSS method --- convexity --- least square problem --- accretive operators --- signal processing --- point projection --- intersection --- planar algebraic curve --- Newton’s iterative method --- the improved curvature circle algorithm --- systems of nonlinear equations --- King’s family --- order of convergence --- multipoint iterative methods --- nonlinear equations --- Potra–Pták method --- optimal methods --- weight function --- basin of attraction --- engineering applications --- Kung–Traub conjecture --- multipoint iterations --- nonlinear equation --- optimal order --- basins of attraction

Mathematical Modelling in Engineering & Human Behaviour 2018

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ISBN: 9783038978046 9783038978053 Year: Pages: 196 DOI: 10.3390/books978-3-03897-805-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-06-26 10:09:00
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This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.

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