An Inertial Algorithm for Solving Hammerstein Equations

Chidume, C. E.; Adamu, Abubakar; Nnakwe, M. O.

doi:10.3390/sym13030376

Cited by 7 publications

(2 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An algorithm of inertial type is an iterative procedure in which subsequent terms are obtained using the preceding two terms. Many authors have shown numerically that adding the inertial extrapolation term in an existing algorithm improves its performance (see, e.g., [19][20][21][22][23][24]). The inertial technique has successfully been employed as an acceleration process for the FBA and its modifications.…”

Section: Introductionmentioning

confidence: 99%

Approximation method for monotone inclusion problems in real Banach spaces with applications

et al. 2022

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce an inertial Halpern-type iterative algorithm for approximating a zero of the sum of two monotone operators in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the sequence generated by our proposed algorithm is established by means of some new geometric inequalities proved in this paper that are of independent interest. Furthermore, numerical simulations in image restoration and compressed sensing problems are also presented. Finally, the performance of the proposed method is compared with that of some existing methods in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

Approximation method for monotone inclusion problems in real Banach spaces with applications

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several acceleration strategies of the PPA via inertial extrapolation or relaxation has been employed by many authors to improve the performance of the PPA over the years (see, e.g. ; [16], [18]). The following question naturally becomes of interest:…”

Section: Introductionmentioning

confidence: 99%

Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications

ABUBAKAR¹,

POOM²,

DUANGKAMON³

et al. 2022

CJM

View full text Add to dashboard Cite

"In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature."

show abstract

An inertial Halpern-type algorithm involving monotone operators on real Banach spaces with application to image recovery problems

et al. 2022

View full text Add to dashboard Cite

An Inertial Algorithm for Solving Hammerstein Equations

Cited by 7 publications

References 33 publications

Approximation method for monotone inclusion problems in real Banach spaces with applications

Approximation method for monotone inclusion problems in real Banach spaces with applications

Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications

An inertial Halpern-type algorithm involving monotone operators on real Banach spaces with application to image recovery problems

Contact Info

Product

Resources

About