Výsledky vyhledávání - 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

Autoři: Argyros, Ioannis K.

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Argyros, Ioannis K.

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

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/569314

Towards Nonlinearity: The p -Regularity Theory.

Autoři: Bednarczuk, Ewa Brezhneva, Olga Leśniewski, Krzysztof a další

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

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

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

Autoři: Argyros, Ioannis K.

Témata: msc:46G05, msc:47J25, msc:47L05, msc:65J15

Popis souboru: application/pdf

Relation: mr:MR1182964; zbl:Zbl 0771.47035; reference:[1] ARGYROS I. K : Newton-like methods under mild differentiability conditions with error analysis.Bull. Austral. Math. Soc. 37 (1987), 131-147. MR 0926985; reference:[2] BALAZS, M, GOLDNER G.: On the method of the cord and on a modification of it for the solution of nonlinear operator equations.Stud. Cere. Mat. 20 (1968), 981-990. MR 0261778; reference:[3] CHEN X., YAMAMOTO T.: Convergence domains of certain iterative methods for solving nonlinear equations.Numer. Funct. Anal. Optim. 10 (1989), 37-48. Zbl 0645.65028, MR 0978801; reference:[4] DENNIS J. E.: Toward a unified convergence theory for Newton-like methods.In: Nonlinear Functional Analysis and Applications (L. B. Rail, ed.), Academic Press, New York, 1971, pp. 425-472. Zbl 0276.65029, MR 0278556; reference:[5] KANTOROVICH L. V., AKILOV G. P.: Functional Analysis in Normed Spaces.Pergamon Press, New York, 1964. Zbl 0127.06104, MR 0213845; reference:[6] KRASNOLESKII M. A., VAINIKKO G. M., ZABREJKO P. P., al.: The Approximate Solution of Operator Equations.(Russian), Nauka, Moscow, 1969. MR 0259635; reference:[7] POTRA F. A., PTÁK V.: Sharp error bounds for Newton's process.Numer. Math. 34 (1980), 63-72. Zbl 0434.65034, MR 0560794; reference:[8] RALL L. B.: A note on the convergence theory of Newton's method.SIAM J. Numer. Anal. 1 (1974), 34-36. MR 0343599; reference:[9] RHEINBOLDT W. C.: A unified convergence theory for a class of iterative processes.SIAM J. Numer. Anal. 5 (1968), 42-63. Zbl 0155.46701, MR 0225468; reference:[10] RHEINBOLDT W. C.: An adaptive continuation process for solving systems of nonlinear equations.In: Mathematical Models and Numerical Methods. (A. N. Tikhonov and others, eds.) Banach Center Publications 3, PWN-Polish Scientific Publishers, Warszawa, 1978, pp. 129-142. Zbl 0378.65029, MR 0514377; reference:[11] YAMAMOTO T.: A convergence theorem for Newton-like methods in Banach spaces.Numer. Math. 51 (1987), 545-557. Zbl 0633.65049, MR 0910864; reference:[12] ZABREJKO P. P., NGUEN D. F.: The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates.Numer. Funct. Anal. Optim. 9 (1987), 671-684. Zbl 0627.65069, MR 0895991; reference:[13] ZINCENKO A. I.: Some approximate methods of solving equations with nondifferentiable operators.(Ukrainian), Dopovïdï Akad. Nauk Ukraïn. RSR Ser. A (1963), 156-161. MR 0160096

Dostupnost: http://hdl.handle.net/10338.dmlcz/132917

Computationally relevant generalized derivatives: theory, evaluation and applications.

Autoři: Barton, Paul I. Khan, Kamil A. Stechlinski, Peter a další

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

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

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

Autoři: Singh, Thokchom Budhachandra Panday, Sunil

Zdroj: 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.

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

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

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

Newton-type method for solving generalized inclusion.

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

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

Témata: 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.

Autoři: Rashid, M. H. Yuan, Ya-xiang

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

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

IMPLICIT AUGMENTED LAGRANGIAN AND GENERALIZED OPTIMIZATION.

Autoři: DE MARCHI, ALBERTO

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

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

On the Kantorovich Theory for Nonsingular and Singular Equations.

Autoři: Argyros, Ioannis K. George, Santhosh Regmi, Samundra a další

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

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

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

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

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

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

A Rigorous Implicit C1 Chebyshev Integrator for Delay Equations.

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

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

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

Parametric Proximal-Point Methods.

Autoři: Pavel, N. Raykov, I.

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

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

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

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

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

Newton-like methods for efficient solutions in vector optimization.

Autoři: Chuong, Thai

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

Témata: VECTOR analysis, MATHEMATICAL optimization, HILBERT space, BANACH spaces, MATHEMATICAL analysis

A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction.

Autoři: Kansal, Munish Sharma, Vanita Rani, Litika a další

Zdroj: AIMS Mathematics; 2024, Vol. 9 Issue 12, p1-37, 37p

Témata: NONLINEAR equations, NUMERICAL analysis, MULTIPLICITY (Mathematics), ELECTRONS, EQUATIONS

Fractals as Julia sets of a exp[dsin(zⁿ)]–bz + c via Jungck four-step iterative method with s-convexity as well as four-step iterative method.

Autoři: Ahmad, Iqbal Sajid, Mohammad Ahmad, Rais

Zdroj: Results in Nonlinear Analysis; 2024, Vol. 7 Issue 3, p1-18, 18p

Témata: FRACTALS, ALGORITHMS, SIN, MANUSCRIPTS, COLOR

Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces.

Autoři: Wang, Xiuhua Kou, Jisheng Gu, Chuanqing

Zdroj: Journal of Optimization Theory & Applications; Jun2012, Vol. 153 Issue 3, p779-793, 15p

Témata: NONLINEAR theories, BANACH spaces, POINT mappings (Mathematics), ITERATIVE methods (Mathematics), EQUATIONS, LIPSCHITZ spaces

Parametric Method for Global Optimization^1,2.

Autoři: MARCHI, S. DE RAYKOV, I.

Zdroj: Journal of Optimization Theory & Applications; Sep2006, Vol. 130 Issue 3, p409-428, 20p, 2 Charts

Témata: MATHEMATICAL optimization, HILBERT space, LIPSCHITZ spaces, ALGORITHMS, ITERATIVE methods (Mathematics), BANACH spaces, HYPERSPACE, FUNCTION spaces, NUMERICAL analysis