Two-step Ulm-type method for solving nonlinear operator equations

Wei Ma; Liuqing Hua

doi:10.2298/fil2103723m

Two-step Ulm-type method for solving nonlinear operator equations

Filomat ◽

10.2298/fil2103723m ◽

2021 ◽

Vol 35 (3) ◽

pp. 723-730

Author(s):

Wei Ma ◽

Liuqing Hua

Keyword(s):

Convergence Rate ◽

Nonlinear Equations ◽

Nonlinear Operator ◽

New Method ◽

Systems Of Nonlinear Equations ◽

Operator Equations ◽

Type Method ◽

Jacobian Matrices ◽

Nonlinear Operator Equations

In this paper, we present a two-step Ulm-type method to solve systems of nonlinear equations without computing Jacobian matrices and solving Jacobian equations. we prove that the two-step Ulm-type method converges locally to the solution with R-convergence rate 3. Numerical implementations demonstrate the effectiveness of the new method.

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Sourcewise representation of solutions to nonlinear operator equations in a Banach space and convergence rate estimates for a regularized Newton’s method

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip.2001.9.4.349 ◽

2001 ◽

Vol 9 (4) ◽

Cited By ~ 1

Author(s):

A. B. Bakushinskii ◽

M.Yu. Kokurin

Keyword(s):

Banach Space ◽

Convergence Rate ◽

Newton’S Method ◽

Newton's Method ◽

Nonlinear Operator ◽

Operator Equations ◽

Nonlinear Operator Equations ◽

Representation Of Solutions

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Continuous modified Newton’s-type method for nonlinear operator equations

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/s10231-002-0054-0 ◽

2003 ◽

Vol 182 (1) ◽

pp. 37-52 ◽

Cited By ~ 9

Author(s):

Alexander G. Ramm ◽

Alexandra B. Smirnova ◽

Angelo Favini

Keyword(s):

Nonlinear Operator ◽

Operator Equations ◽

Type Method ◽

Nonlinear Operator Equations

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The midpoint method for solving nonlinear operator equations in Banach space

Applied Mathematics Letters ◽

10.1016/0893-9659(92)90076-l ◽

1992 ◽

Vol 5 (4) ◽

pp. 7-9 ◽

Cited By ~ 10

Author(s):

Dong Chen ◽

Ioannis K. Argyros

Keyword(s):

Banach Space ◽

Nonlinear Operator ◽

Operator Equations ◽

Nonlinear Operator Equations ◽

Midpoint Method

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Iterations converging to distinct solutions of some nonlinear operator equations in Banach space

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117128600073x ◽

1986 ◽

Vol 9 (3) ◽

pp. 583-587

Author(s):

Ioannis K. Argyros

Keyword(s):

Banach Space ◽

Linear Operator ◽

Nonlinear Operator ◽

Operator Equations ◽

Nonlinear Operator Equations

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k times−=y, k=2,3,…whereMkis ak-linear operator on a Banach spaceXandy∈Xis fixed.

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The exact solution for solving a class nonlinear operator equations in the reproducing kernel space

Applied Mathematics and Computation ◽

10.1016/s0096-3003(02)00370-3 ◽

2003 ◽

Vol 143 (2-3) ◽

pp. 393-399 ◽

Cited By ~ 55

Author(s):

Chun-li Li ◽

Ming-gen Cui

Keyword(s):

Exact Solution ◽

Nonlinear Operator ◽

Reproducing Kernel ◽

Kernel Space ◽

Reproducing Kernel Space ◽

Operator Equations ◽

Nonlinear Operator Equations

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Solvability and Galerkin Approximations of a Class of Nonlinear Operator Equations

Zeitschrift für Analysis und ihre Anwendungen ◽

10.4171/zaa/1107 ◽

2002 ◽

Vol 21 (3) ◽

pp. 761-781 ◽

Cited By ~ 32

Author(s):

Gabrie Gatica

Keyword(s):

Nonlinear Operator ◽

Operator Equations ◽

Nonlinear Operator Equations ◽

Galerkin Approximations

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Nonstationary iteeative solution of nonlinear operator equations

Ukrainian Mathematical Journal ◽

10.1007/bf01085462 ◽

1974 ◽

Vol 25 (4) ◽

pp. 453-457

Author(s):

T. S. Kurchenko ◽

N. A. Ksendz

Keyword(s):

Nonlinear Operator ◽

Operator Equations ◽

Nonlinear Operator Equations

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Existence of solutions for nonlinear operator equations

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2019180 ◽

2019 ◽

Vol 39 (8) ◽

pp. 4429-4441

Author(s):

Yucheng Bu ◽

◽

Yujun Dong ◽

Keyword(s):

Nonlinear Operator ◽

Existence Of Solutions ◽

Operator Equations ◽

Nonlinear Operator Equations

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Numerical verification of existence and inclusion of solutions for nonlinear operator equations

Journal of Computational and Applied Mathematics ◽

10.1016/0377-0427(94)00090-n ◽

1995 ◽

Vol 60 (1-2) ◽

pp. 171-185 ◽

Cited By ~ 18

Author(s):

Shin'ichi Oishi

Keyword(s):

Nonlinear Operator ◽

Numerical Verification ◽

Operator Equations ◽

Nonlinear Operator Equations

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The Existence of Solutions for Nonlinear Operator Equations

Georgian Mathematical Journal ◽

10.1515/gmj.2008.45 ◽

2008 ◽

Vol 15 (1) ◽

pp. 45-52

Author(s):

Marek Galewski

Keyword(s):

Nonlinear Operator ◽

Existence Of Solutions ◽

Existence Results ◽

Nonlinear Operator Equation ◽

Global Minima ◽

Operator Equations ◽

Nonlinear Operator Equations ◽

Dual Variational Method ◽

Dual Action ◽

Primal And Dual

Abstract We provide the existence results for a nonlinear operator equation Λ*Φ′ (Λ𝑥) = 𝐹′(𝑥), in case 𝐹 – Φ is not necessarily convex. We introduce the dual variational method which is based on finding global minima of primal and dual action functionals on certain nonlinear subsets of their domains and on investigating relations between the minima obtained. The solution is a limit of a minimizng sequence whose existence and convergence are proved. The application for the non-convex Dirichlet problem with P.D.E. is given.

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