scholarly journals A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 18262-18277
Author(s):  
Auwal Bala Abubakar ◽  
Kanikar Muangchoo ◽  
Abdulkarim Hassan Ibrahim ◽  
Abubakar Bakoji Muhammad ◽  
Lateef Olakunle Jolaoso ◽  
...  
Keyword(s):  
Image Restoration ◽  
Monotone Operator ◽  
Operator Equations ◽  
Type Method

PRP-like algorithm for monotone operator equations

2021 ◽  
Author(s):  
Auwal Bala Abubakar ◽  
Poom Kumam ◽  
Hassan Mohammad ◽  
Abdulkarim Hassan Ibrahim
Keyword(s):  
Monotone Operator ◽  
Operator Equations

scholarly journals Derivative-free HS-DY-type method for solving nonlinear equations and image restoration

Heliyon ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. e05400
Author(s):  
Auwal Bala Abubakar ◽  
Poom Kumam ◽  
Abdulkarim Hassan Ibrahim ◽  
Jewaidu Rilwan
Keyword(s):  
Image Restoration ◽  
Nonlinear Equations ◽  
Type Method ◽  
Derivative Free

scholarly journals Inertial Mann-Type Algorithm for a Nonexpansive Mapping to Solve Monotone Inclusion and Image Restoration Problems

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 750
Author(s):  
Natthaphon Artsawang ◽  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Image Restoration ◽  
Zero Point ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Type Method ◽  
Type Algorithm ◽  
Inertial Terms

In this article, we establish a new Mann-type method combining both inertial terms and errors to find a fixed point of a nonexpansive mapping in a Hilbert space. We show strong convergence of the iterate under some appropriate assumptions in order to find a solution to an investigative fixed point problem. For the virtue of the main theorem, it can be applied to an approximately zero point of the sum of three monotone operators. We compare the convergent performance of our proposed method, the Mann-type algorithm without both inertial terms and errors, and the Halpern-type algorithm in convex minimization problem with the constraint of a non-zero asymmetric linear transformation. Finally, we illustrate the functionality of the algorithm through numerical experiments addressing image restoration problems.

A derivative-free iterative method for nonlinear ill-posed equations with monotone operators

2017 ◽  
Vol 25 (5) ◽  
pp. 543-551 ◽  
Author(s):  
Santhosh George ◽  
M. Thamban Nair
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Monotone Operator ◽  
Regularization Parameter ◽  
A Priori ◽  
Monotone Operators ◽  
Adaptive Procedure ◽  
Operator Equations ◽  
Derivative Free ◽  
Ill Posed

AbstractRecently, Semenova [12] considered a derivative free iterative method for nonlinear ill-posed operator equations with a monotone operator. In this paper, a modified form of Semenova’s method is considered providing simple convergence analysis under more realistic nonlinearity assumptions. The paper also provides a stopping rule for the iteration based on an a priori choice of the regularization parameter and also under the adaptive procedure considered by Pereverzev and Schock [11].

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