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Signal recovery and polynomiographic visualization of modified Noor iteration of operators with property (E)

Paimsang Papinwich, Thianwan Tanakit

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240070

This article aims to provide a modified Noor iterative scheme to approximate the fixed points of generalized nonexpansive mappings with property (E) called MN-iteration. We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical experiments of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Ultimately, an illustrative analysis regarding Noor, SP-, and MN-iteration procedures is obtained via polysomnographic techniques. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. The obtained graphs describe the pattern of complex polynomials and also the convergence properties of the iterative method. They can also be used to increase the functionality of the existing polynomiography software.