Iterative Methods for Solving Nonlinear Equations and Systems

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

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.