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: | , , |
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| Format: | Online |
| Jezik: | engleski |
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MDPI - Multidisciplinary Digital Publishing Institute
2021
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| Online pristup: | 43212 |
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| _version_ | 1869516126132633600 |
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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. |
| format | Online |
| id | doab-20.500.12854ir-50741 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| 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 |
| work_keys_str_mv | AT soleymanifazlollah iterativemethodsforsolvingnonlinearequationsandsystems AT corderoalicia iterativemethodsforsolvingnonlinearequationsandsystems AT torregrosajuanr iterativemethodsforsolvingnonlinearequationsandsystems |