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

2001 ◽  
Vol 9 (4) ◽  
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

scholarly journals Semilocal analysis of equations with smooth operators

1981 ◽  
Vol 4 (3) ◽  
pp. 553-563 ◽  
Author(s):  
George J. Miel
Keyword(s):  
Recent Work ◽  
Error Bounds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Kantorovich Theorem ◽  
Refined Version

Recent work on semilocal analysis of nonlinear operator equations is informally reviewed. A refined version of the Kantorovich theorem for Newton's method, with new error bounds, is presented. Related topics are briefly surveyed.

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

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.

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

Filomat ◽  
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.

scholarly journals Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rongfei Lin ◽  
Yueqing Zhao ◽  
Qingbiao Wu ◽  
Jueliang Hu
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Convergence Theorems ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Numerical Examples ◽  
Halley’S Method ◽  
Halley's Method

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.

scholarly journals AN ERROR ANALYSIS FOR THE MIDPOINT METHOD

1999 ◽  
Vol 30 (2) ◽  
pp. 71-83
Author(s):  
IOANNIS K. ARGYROS
Keyword(s):  
Banach Space ◽  
Error Analysis ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Space Setting ◽  
Midpoint Method

We approximate zeros of nonlinear operator equations in Banach space setting using Newton-Kantrorvich assumptions and the majorant theory for the midpoint method.

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