Heart disease detection using inertial Mann relaxed CQ algorithms for split feasibility problems

This study investigates the weak convergence of the sequences generated by the inertial relaxed $CQ$ algorithm with Mann's iteration for solving the split feasibility problem in real Hilbert spaces. Moreover, we present the advantage of our algorithm by choosing a wider range of parameters than the recent methods. Finally, we apply our algorithm to solve the classification problem using the heart disease dataset collected from the UCI machine learning repository as a training set. The result shows that our algorithm performs better than many machine learning methods and also extreme learning machine with fast iterative shrinkage-thresholding algorithm (FISTA) and inertial relaxed $CQ$ algorithm (IRCQA) under consideration according to accuracy, precision, recall, and F1-score

A Hybrid Method for a Countable Family of Multivalued Maps, Equilibrium Problems, and Variational Inequality Problems

We introduce a new monotone hybrid iterative scheme for finding a common element of the set of common fixed points of a countable family of nonexpansive multivalued maps, the set of solutions of variational inequality problem, and the set of the solutions of the equilibrium problem in a Hilbert space. Strong convergence theorems of the purposed iteration are established

Modified Projection Method with Inertial Technique and Hybrid Stepsize for the Split Feasibility Problem

We designed a modified projection method with a new condition of the inertial step and the step size for the split feasibility problem in Hilbert spaces. We show that our iterate weakly converged to a solution. Lastly, we give numerical examples and comparisons that could be applied to signal recovery to show the efficiency of our method

Parallel Hybrid Algorithms for a Finite Family of <i>G</i>-Nonexpansive Mappings and Its Application in a Novel Signal Recovery

This article considers a parallel monotone hybrid algorithm for a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graphs and suggests iterative schemes for finding a common fixed point by the two different hybrid projection methods. Moreover, we show the computational performance of our algorithm in comparison to some methods. Strong convergence theorems are proved under suitable conditions. Finally, we give some numerical experiments of our algorithms to show the efficiency and implementation of the LASSO problems in signal recovery with different types of blurred matrices and noise

Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003)

Modified Projection Method with Inertial Technique and Hybrid Stepsize for the Split Feasibility Problem

We designed a modified projection method with a new condition of the inertial step and the step size for the split feasibility problem in Hilbert spaces. We show that our iterate weakly converged to a solution. Lastly, we give numerical examples and comparisons that could be applied to signal recovery to show the efficiency of our method

The modified extragradient method for nonexpansive multivalued mappings and variational inequality problems

[[abstract]]In this paper, we prove the strong convergence of an approximating common element of the set of fixed points of a nonexpansive multivalued mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping in a Hilbert space by using the modified extragradient method. As applications, we give the example and numerical results for supporting our main theorem

Breast Cancer Screening Using a Modified Inertial Projective Algorithms for Split Feasibility Problems

To detect breast cancer in mammography screening practice, we modify the inertial relaxed CQ algorithm with Mann’s iteration for solving split feasibility problems in real Hilbert spaces to apply in an extreme learning machine as an optimizer. Weak convergence of the proposed algorithm is proved under certain mild conditions. Moreover, we present the advantage of our algorithm by comparing it with existing machine learning methods. The highest performance value of 85.03% accuracy, 82.56% precision, 87.65% recall, and 85.03% F1-score show that our algorithm performs better than the other machine learning models

A Convergent Algorithm for Equilibrium Problem to Predict Prospective Mathematics Teachers&rsquo; Technology Integrated Competency

Educational data classification has become an effective tool for exploring the hidden pattern or relationship in educational data and predicting students&rsquo; performance or teachers&rsquo; competency. This study proposes a new method based on machine learning algorithms to predict the technology-integrated competency of pre-service mathematics teachers. In this paper, we modified the inertial subgradient extragradient algorithm for pseudomonotone equilibrium and proved the weak convergence theorem under some suitable conditions in Hilbert spaces. We then applied to solve data classification by extreme learning machine using the dataset comprised of the technology-integrated competency of 954 pre-service mathematics teachers in a university in northern Thailand, longitudinally collected for five years. The flexibility of our algorithm was shown by comparisons of the choice of different parameters. The performance was calculated and compared with the existing algorithms to be implemented for prediction. The results show that the proposed method achieved a classification accuracy of 81.06%. The predictions were implemented using ten attributes, including demographic information, skills, and knowledge relating to technology developed throughout the teacher education program. Such data driven studies are significant for establishing a prospective teacher competency analysis framework in teacher education and contributing to decision-making for policy design

A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications

In this work, we aim to prove the strong convergence of the sequence generated by the modified inertial parallel viscosity-type algorithm for finding a common fixed point of a finite family of nonexpansive mappings under mild conditions in real Hilbert spaces. Moreover, we present the numerical experiments to solve linear systems and differential problems using Gauss–Seidel, weight Jacobi, and successive over relaxation methods. Furthermore, we provide our algorithm to show the efficiency and implementation of the LASSO problems in signal recovery. The novelty of our algorithm is that we show that the algorithm is efficient compared with the existing algorithms