Iterative Methods and Their Dynamics with Applications

DOI10.1201/9781315153469zbMath1360.65005OpenAlexW4289984654MaRDI QIDQ2951813

Ángel Alberto Magreñán, Ioannis K. Argyros

Publication date: 10 January 2017

Full work available at URL: https://doi.org/10.1201/9781315153469

Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (76)

Secant-like methods for solving nonlinear models with applications to chemistry ⋮ Improved semilocal convergence analysis in Banach space with applications to chemistry ⋮ Ball convergence of a sixth-order Newton-like method based on means under weak conditions ⋮ Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations ⋮ An excellent derivative-free multiple-zero finding numerical technique of optimal eighth order convergence ⋮ Unified convergence analysis of frozen Newton-like methods under generalized conditions ⋮ Unified semi-local convergence for $k$-step iterative methods with flexible and frozen linear operator ⋮ Ball convergence of an efficient eighth order iterative method under weak conditions ⋮ Extending the domain of starting points for Newton's method under conditions on the second derivative ⋮ On a two-step Kurchatov-type method in Banach space ⋮ Convergence analysis of a fifth-order iterative method using recurrence relations and conditions on the first derivative ⋮ Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions ⋮ Extending the applicability of a seventh order method without inverses of derivatives under weak conditions ⋮ Extended two-step-Kurchatov method for solving Banach space valued nondifferentiable equations ⋮ A Class of Higher-Order Newton-Like Methods for Systems of Nonlinear Equations ⋮ On the complexity of convergence for high order iterative methods ⋮ On the convergence of a novel seventh convergence order schemes for solving equations ⋮ A ball comparison between extended modified Jarratt methods under the same set of conditions for solving equations and systems of equations ⋮ Unnamed Item ⋮ Ball convergence of an efficient multi-step scheme for solving equations and systems of equations ⋮ Convergence analysis of the Gauss-Newton-Potra method for nonlinear least squares problems ⋮ A study of the local convergence of a derivative free method in Banach spaces ⋮ Unified ball convergence of third and fourth convergence order algorithms under $omega-$continuity conditions ⋮ Expanding the applicability of Stirling's method under weaker conditions and restricted convergence regions ⋮ Iterative convergence with Banach space valued functions in abstract fractional calculus ⋮ Expanding the applicability of four iterative methods for solving least squares problems ⋮ On the convergence of Newton-like MS method with dynamics and applications ⋮ The eigenspace spectral regularization method for solving discrete ill-posed systems ⋮ Local and semi-local convergence for Chebyshev two point like methods with applications in different fields ⋮ Extended local convergence and comparisons for two three-step Jarratt-type methods under the same conditions ⋮ A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems ⋮ Higher order Traub-Steffensen type methods and their convergence analysis in Banach spaces ⋮ Extended convergence ball for an efficient eighth order method using only the first derivative ⋮ Ball comparison between Jarratt’s and other fourth order method for solving equations ⋮ On the convergence of Kurchatov-type methods using recurrent functions for solving equations ⋮ EXTENDING THE APPLICABILITY OF INEXACT GAUSS-NEWTON METHOD FOR SOLVING UNDERDETERMINED NONLINEAR LEAST SQUARES PROBLEMS ⋮ A faster King–Werner-type iteration and its convergence analysis ⋮ Extending the Kantorovich's theorem on Newton's method for solving strongly regular generalized equation ⋮ Kantorovich-Like Convergence Theorems for Newton’s Method Using Restricted Convergence Domains ⋮ Newton-like methods with increasing order of convergence and their convergence analysis in Banach space ⋮ Newton-Type Solvers Using Outer Inverses for Singular Equations ⋮ Comparison between some sixth convergence order solvers ⋮ Local comparison between two-step methods under the same conditions ⋮ Unnamed Item ⋮ Extended semilocal convergence for the Newton-Kurchatov method ⋮ On the approximation of $m$th power divided differences preserving the local order of convergence ⋮ Unnamed Item ⋮ Extended local convergence for some inexact methods with applications ⋮ Two-step solver for equations with nondifferentiable term ⋮ Two-step solver for nonlinear equations ⋮ Generalized Kung-Traub method and its multi-step iteration in Banach spaces ⋮ Ball comparison between four fourth convergence order methods under the same set of hypotheses for solving equations ⋮ Local convergence for an almost sixth order method for solving equations under weak conditions ⋮ Generalized iterative procedures and their applications to Banach space valued functions in abstract fractional calculus ⋮ On the complexity of extending the convergence region for Traub's method ⋮ On the complexity of extending the convergence ball of Wang's method for finding a zero of a derivative ⋮ Weaker 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methods under generalized conditions for nonlinear equations ⋮ Extending the usage of Newton's method with applications to the solution of Bratu's equation ⋮ Local convergence analysis of two iterative methods ⋮ An efficient class of Traub-Steffensen-like seventh order multiple-root solvers with applications ⋮ Extended local and semilocal convergence for interpolatory iterative methods for nonlinear equations ⋮ An optimal 8th order Newton's-type method with basin of attraction ⋮ On a novel seventh convergence order method for solving nonlinear equations and its extensions ⋮ Extended convergence analysis of the Newton–Potra method under weak conditions

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