Search Results - Newton-like method to approximate implicit functions in a Banach space

On an application of a Newton-like method to the approximation of implicit functions

Authors: Argyros, Ioannis K.

Subject Terms: Newton-like method to approximate implicit functions in a Banach space, Extrapolation to the limit, deferred corrections, Derivatives of functions in infinite-dimensional spaces, Iterative procedures involving nonlinear operators, approximate implicit functions in a Banach space, Numerical solutions to equations with nonlinear operators, error bounds, Linear spaces of operators, linear algebraic system of finite order, Newton-like method

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Access URL: https://zbmath.org/1657752
https://zbmath.org/90609

On an application of a modification of a Newton-like method to the approximation of implicit functions

Authors: Argyros, Ioannis K.

Subject Terms: Banach space, implicit function, convergence, Iterative procedures involving nonlinear operators, Numerical solutions to equations with nonlinear operators, operator equation, error bounds, Newton-like method

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Access URL: https://zbmath.org/569314

Towards Nonlinearity: The p -Regularity Theory.

Authors: Bednarczuk, Ewa Brezhneva, Olga Leśniewski, Krzysztof et al.

Source: Entropy; May2025, Vol. 27 Issue 5, p518, 46p

Subject Terms: NONLINEAR differential equations, IMPLICIT functions, PARTIAL differential equations, DIFFERENTIAL equations, BOUNDARY value problems

Extended Newton-type method for nonlinear functions with values in a cone.

Authors: Silva, G. N. Santos, P. S. M. Souza, S. S.

Source: Computational & Applied Mathematics; Sep2018, Vol. 37 Issue 4, p5082-5097, 16p

Subject Terms: NEWTON-Raphson method, BANACH spaces, STOCHASTIC convergence, DIFFERENTIABLE functions, KANTOROVICH method

Generalized iterative procedures and their applications to Banach space valued functions in abstract fractional calculus.

Authors: Anastassiou, George A. Argyros, Ioannis K.

Source: SeMA Journal; Jun2018, Vol. 75 Issue 2, p215-227, 13p

Newton-like methods for efficient solutions in vector optimization.

Authors: Chuong, Thai

Source: Computational Optimization & Applications; Apr2013, Vol. 54 Issue 3, p495-516, 22p

Subject Terms: VECTOR analysis, MATHEMATICAL optimization, HILBERT space, BANACH spaces, MATHEMATICAL analysis

Newton Methods with Hölder Derivative.

Authors: Ahues, Mario

Source: Numerical Functional Analysis & Optimization; Aug/Sep2004, Vol. 25 Issue 5/6, p379-395, 17p

Subject Terms: BANACH spaces, GENERALIZED spaces, BOUNDARY value problems, COMPLEX variables, TOPOLOGY, MATHEMATICS

Torus knot choreographies in the n-body problem.

Authors: Calleja, Renato García-Azpeitia, Carlos Lessard, Jean-Philippe et al.

Source: Nonlinearity; Jan2021, Vol. 34 Issue 1, p1-37, 37p

Subject Terms: MANY-body problem, DELAY differential equations, TORUS, BANACH spaces, PERIODIC motion

On the convergence of the midpoint method.

Authors: Ioannis Argyros Livinus Uko

Source: Numerical Algorithms; Feb2008, Vol. 47 Issue 2, p157-167, 11p

Subject Terms: NONLINEAR statistical models, NONLINEAR evolution equations, ACCELERATION of convergence in numerical analysis, BANACH algebras

On a non-smooth version of Newton's method based on Hölderian assumptions.

Authors: Argyros, IoannisK.

Source: International Journal of Computer Mathematics; Dec2007, Vol. 84 Issue 12, p1747-1756, 10p

Subject Terms: NEWTON-Raphson method, EQUATIONS, INTEGRAL equations, FUNCTIONAL equations, ITERATIVE methods (Mathematics)

Computationally relevant generalized derivatives: theory, evaluation and applications.

Authors: Barton, Paul I. Khan, Kamil A. Stechlinski, Peter et al.

Source: Optimization Methods & Software; Aug-Dec2018, Vol. 33 Issue 4-6, p1030-1072, 43p

Subject Terms: AUTOMATIC differentiation, ROBUST optimization, NONSMOOTH optimization, SENSITIVITY analysis, STOCHASTIC partial differential equations

On a nonsmooth version of Newton’s method using locally lipschitzian operators.

Authors: Argyros, Ioannis

Source: Rendiconti del Circolo Matematico di Palermo (Series 2); Feb2007, Vol. 56 Issue 1, p5-16, 12p

Dynamical and convergence analysis of a new memory-based iterative method.

Authors: Singh, Thokchom Budhachandra Panday, Sunil

Source: Journal of Applied Mathematics & Computing; Oct2025, Vol. 71 Issue 5, p7205-7223, 19p

BROYDEN QUASI-NEWTON SECANT-TYPE METHOD FOR SOLVING CONSTRAINED MIXED GENERALIZED EQUATIONS.

Authors: DA SILVA JUNIOR, P. C. FERREIRA, O. P. SILVA, G. N.

Source: Journal of Nonlinear & Variational Analysis; 2025, Vol. 9 Issue 4, p523-538, 16p

Subject Terms: QUASI-Newton methods, LIPSCHITZ continuity, EQUATIONS, ITERATIVE methods (Mathematics)

Newton-type method for solving generalized inclusion.

Authors: Santos, P. S. M. Silva, G. N. Silva, R. C. M.

Source: Numerical Algorithms; Dec2021, Vol. 88 Issue 4, p1811-1829, 19p

Subject Terms: HOLDER spaces, BANACH spaces, NONLINEAR equations, PROBLEM solving, CONTINUOUS functions, NEWTON-Raphson method, DIFFERENTIABLE functions

Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings.

Authors: Rashid, M. H. Yuan, Ya-xiang

Source: Applicable Analysis; 2022, Vol. 101 Issue 1, p14-34, 21p

Subject Terms: SET-valued maps, BANACH spaces, NEWTON-Raphson method, DIFFERENTIABLE functions, EQUATIONS, REGULAR graphs

IMPLICIT AUGMENTED LAGRANGIAN AND GENERALIZED OPTIMIZATION.

Authors: DE MARCHI, ALBERTO

Source: Journal of Applied & Numerical Optimization; 2024, Vol. 6 Issue 2, p291-320, 30p

Subject Terms: NONLINEAR programming, LAGRANGIAN functions, CALCULUS of variations, MULTIPLIER (Economics), ECONOMICS

On the Kantorovich Theory for Nonsingular and Singular Equations.

Authors: Argyros, Ioannis K. George, Santhosh Regmi, Samundra et al.

Source: Axioms (2075-1680); Jun2024, Vol. 13 Issue 6, p358, 13p

Subject Terms: BANACH spaces, LINEAR operators, NEWTON-Raphson method, EQUATIONS, HILBERT space, NONLINEAR equations

A Rigorous Implicit C1 Chebyshev Integrator for Delay Equations.

Authors: Lessard, Jean-Philippe James, J. D. Mireles

Source: Journal of Dynamics & Differential Equations; Dec2021, Vol. 33 Issue 4, p1959-1988, 30p

Subject Terms: NEWTON-Raphson method, NUMERICAL integration, EQUATIONS, SYSTEM integration, DELAY differential equations

Parametric Proximal-Point Methods.

Authors: Pavel, N. Raykov, I.

Source: Journal of Optimization Theory & Applications; Oct2008, Vol. 139 Issue 1, p85-107, 23p, 4 Diagrams, 4 Charts, 1 Graph

Subject Terms: CONVEX functions, REAL variables, SUBDIFFERENTIALS, DIFFERENTIABLE functions, COMPLEX variables, HILBERT space, BAIRE classes, CONCAVE functions, BANACH spaces, HYPERSPACE