Iterative Methods for Solving Nonlinear Equations and Systems

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...

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Bibliographic Details
Main Author: Soleymani, Fazlollah (auth)
Other Authors: Cordero, Alicia (auth), Torregrosa, Juan R. (auth)
Format: Electronic Book Chapter
Language:English
Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
Subjects:
PDE
Online Access:DOAB: download the publication
DOAB: description of the publication
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100 1 |a Soleymani, Fazlollah  |4 auth 
700 1 |a Cordero, Alicia  |4 auth 
700 1 |a Torregrosa, Juan R.  |4 auth 
245 1 0 |a Iterative Methods for Solving Nonlinear Equations and Systems 
260 |b MDPI - Multidisciplinary Digital Publishing Institute  |c 2019 
300 |a 1 electronic resource (494 p.) 
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520 |a 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. 
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546 |a English 
653 |a Lipschitz condition 
653 |a heston model 
653 |a rectangular matrices 
653 |a computational efficiency 
653 |a Hull-White 
653 |a order of convergence 
653 |a signal and image processing 
653 |a dynamics 
653 |a divided difference operator 
653 |a engineering applications 
653 |a smooth and nonsmooth operators 
653 |a Newton-HSS method 
653 |a higher order method 
653 |a Moore-Penrose 
653 |a asymptotic error constant 
653 |a multiple roots 
653 |a higher order 
653 |a efficiency index 
653 |a multiple-root finder 
653 |a computational efficiency index 
653 |a Potra-Pták method 
653 |a nonlinear equations 
653 |a system of nonlinear equations 
653 |a purely imaginary extraneous fixed point 
653 |a attractor basin 
653 |a point projection 
653 |a fixed point theorem 
653 |a convex constraints 
653 |a weight function 
653 |a radius of convergence 
653 |a Frédholm integral equation 
653 |a semi-local convergence 
653 |a nonlinear HSS-like method 
653 |a convexity 
653 |a accretive operators 
653 |a Newton-type methods 
653 |a multipoint iterations 
653 |a banach space 
653 |a Kantorovich hypothesis 
653 |a variational inequality problem 
653 |a Newton method 
653 |a semilocal convergence 
653 |a least square problem 
653 |a Fréchet derivative 
653 |a Newton's method 
653 |a iterative process 
653 |a Newton-like method 
653 |a Banach space 
653 |a sixteenth-order optimal convergence 
653 |a nonlinear systems 
653 |a Chebyshev-Halley-type 
653 |a Jarratt method 
653 |a iteration scheme 
653 |a Newton's iterative method 
653 |a basins of attraction 
653 |a drazin inverse 
653 |a option pricing 
653 |a higher order of convergence 
653 |a non-linear equation 
653 |a numerical experiment 
653 |a signal processing 
653 |a optimal methods 
653 |a rate of convergence 
653 |a n-dimensional Euclidean space 
653 |a non-differentiable operator 
653 |a projection method 
653 |a Newton's second order method 
653 |a intersection 
653 |a planar algebraic curve 
653 |a Hilbert space 
653 |a conjugate gradient method 
653 |a sixteenth order convergence method 
653 |a Padé approximation 
653 |a optimal iterative methods 
653 |a error bound 
653 |a high order 
653 |a Fredholm integral equation 
653 |a global convergence 
653 |a iterative method 
653 |a integral equation 
653 |a ?-continuity condition 
653 |a systems of nonlinear equations 
653 |a generalized inverse 
653 |a local convergence 
653 |a iterative methods 
653 |a multi-valued quasi-nonexpasive mappings 
653 |a R-order 
653 |a finite difference (FD) 
653 |a nonlinear operator equation 
653 |a basin of attraction 
653 |a PDE 
653 |a King's family 
653 |a Steffensen's method 
653 |a nonlinear monotone equations 
653 |a Picard-HSS method 
653 |a nonlinear models 
653 |a the improved curvature circle algorithm 
653 |a split variational inclusion problem 
653 |a computational order of convergence 
653 |a with memory 
653 |a multipoint iterative methods 
653 |a Kung-Traub conjecture 
653 |a multiple zeros 
653 |a fourth order iterative methods 
653 |a parametric curve 
653 |a optimal order 
653 |a nonlinear equation 
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856 4 0 |a www.oapen.org  |u https://directory.doabooks.org/handle/20.500.12854/50741  |7 0  |z DOAB: description of the publication