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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Glavni autori: Soleymani, Fazlollah, Cordero, Alicia, Torregrosa, Juan R.
Format: Online
Jezik:engleski
Izdano: MDPI - Multidisciplinary Digital Publishing Institute 2021
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Online pristup:43212
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author Soleymani, Fazlollah
Cordero, Alicia
Torregrosa, Juan R.
author_browse Cordero, Alicia
Soleymani, Fazlollah
Torregrosa, Juan R.
author_facet Soleymani, Fazlollah
Cordero, Alicia
Torregrosa, Juan R.
author_sort Soleymani, Fazlollah
collection Directory of Open Access Books
description 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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spelling doab-20.500.12854ir-507412023-12-20T18:40:38Z Iterative Methods for Solving Nonlinear Equations and Systems Soleymani, Fazlollah Cordero, Alicia Torregrosa, Juan R. QA1-939 Q1-390 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 bic Book Industry Communication::P Mathematics & science 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. 2021-02-11T16:46:34Z 2021-02-11T16:46:34Z 2020-01-07 09:08:26 2019 book 43212 9783039219414 9783039219407 https://directory.doabooks.org/handle/20.500.12854/50741 eng application/octet-stream Attribution-NonCommercial-NoDerivatives 4.0 International https://mdpi.com/books/pdfview/book/1877 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03921-941-4 10.3390/books978-3-03921-941-4 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783039219414 9783039219407 494 open access
spellingShingle QA1-939
Q1-390
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
bic Book Industry Communication::P Mathematics & science
Soleymani, Fazlollah
Cordero, Alicia
Torregrosa, Juan R.
Iterative Methods for Solving Nonlinear Equations and Systems
title Iterative Methods for Solving Nonlinear Equations and Systems
title_full Iterative Methods for Solving Nonlinear Equations and Systems
title_fullStr Iterative Methods for Solving Nonlinear Equations and Systems
title_full_unstemmed Iterative Methods for Solving Nonlinear Equations and Systems
title_short Iterative Methods for Solving Nonlinear Equations and Systems
title_sort iterative methods for solving nonlinear equations and systems
topic QA1-939
Q1-390
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
bic Book Industry Communication::P Mathematics & science
topic_facet QA1-939
Q1-390
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
bic Book Industry Communication::P Mathematics & science
url 43212
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AT corderoalicia iterativemethodsforsolvingnonlinearequationsandsystems
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