TY - BOOK
ID - 43212
TI - Iterative Methods for Solving Nonlinear Equations and Systems
AU - Torregrosa, Juan R.
AU - Cordero, Alicia
AU - Soleymani, Fazlollah
PB - MDPI - Multidisciplinary Digital Publishing Institute
PY - 2019
KW - point projection
KW - intersection
KW - parametric curve
KW - n-dimensional Euclidean space
KW - Newton’s second order method
KW - fixed point theorem
KW - nonlinear equations
KW - multiple zeros
KW - optimal iterative methods
KW - higher order of convergence
KW - nonlinear operator equation
KW - Fréchet derivative
KW - ?-continuity condition
KW - Newton-like method
KW - Frédholm integral equation
KW - nonlinear equations
KW - Padé approximation
KW - iterative method
KW - order of convergence
KW - numerical experiment
KW - fourth order iterative methods
KW - local convergence
KW - banach space
KW - radius of convergence
KW - nonlinear equation
KW - iterative process
KW - non-differentiable operator
KW - Lipschitz condition
KW - high order
KW - sixteenth order convergence method
KW - local convergence
KW - dynamics
KW - Banach space
KW - Newton’s method
KW - semi-local convergence
KW - Kantorovich hypothesis
KW - iterative methods
KW - Steffensen’s method
KW - R-order
KW - with memory
KW - computational efficiency
KW - non-linear equation
KW - basins of attraction
KW - optimal order
KW - higher order method
KW - computational order of convergence
KW - nonlinear equations
KW - multiple roots
KW - Chebyshev–Halley-type
KW - optimal iterative methods
KW - efficiency index
KW - Banach space
KW - semilocal convergence
KW - ?-continuity condition
KW - Jarratt method
KW - error bound
KW - Fredholm integral equation
KW - Newton’s method
KW - global convergence
KW - variational inequality problem
KW - split variational inclusion problem
KW - multi-valued quasi-nonexpasive mappings
KW - Hilbert space
KW - sixteenth-order optimal convergence
KW - multiple-root finder
KW - asymptotic error constant
KW - weight function
KW - purely imaginary extraneous fixed point
KW - attractor basin
KW - drazin inverse
KW - generalized inverse
KW - iterative methods
KW - higher order
KW - efficiency index
KW - integral equation
KW - efficiency index
KW - nonlinear models
KW - iterative methods
KW - higher order
KW - nonlinear equations
KW - optimal iterative methods
KW - multiple roots
KW - efficiency index
KW - iterative methods
KW - nonlinear equations
KW - Newton-type methods
KW - smooth and nonsmooth operators
KW - heston model
KW - Hull–White
KW - option pricing
KW - PDE
KW - finite difference (FD)
KW - iteration scheme
KW - Moore–Penrose
KW - rectangular matrices
KW - rate of convergence
KW - efficiency index
KW - nonlinear equations
KW - conjugate gradient method
KW - projection method
KW - convex constraints
KW - signal and image processing
KW - nonlinear monotone equations
KW - conjugate gradient method
KW - projection method
KW - signal processing
KW - nonlinear systems
KW - multipoint iterative methods
KW - divided difference operator
KW - order of convergence
KW - Newton’s method
KW - computational efficiency index
KW - system of nonlinear equations
KW - Newton method
KW - Newton-HSS method
KW - nonlinear HSS-like method
KW - Picard-HSS method
KW - convexity
KW - least square problem
KW - accretive operators
KW - signal processing
KW - point projection
KW - intersection
KW - planar algebraic curve
KW - Newton’s iterative method
KW - the improved curvature circle algorithm
KW - systems of nonlinear equations
KW - King’s family
KW - order of convergence
KW - multipoint iterative methods
KW - nonlinear equations
KW - Potra–Pták method
KW - optimal methods
KW - weight function
KW - basin of attraction
KW - engineering applications
KW - Kung–Traub conjecture
KW - multipoint iterations
KW - nonlinear equation
KW - optimal order
KW - basins of attraction
SN - 9783039219407 9783039219414
AB - 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.
ER -