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...