In the given study, we investigate the three-step NTS’s ball convergence for solving nonlinear operator equations with a convergence order of five in a Banach setting. A nonlinear operator’s first-order derivative is assumed to meet the g...
This article considers the fourth-order family of weighted-Newton methods. It provides the range of initial guesses that ensure the convergence. The analysis is given for Banach space-valued mappings, and the hypotheses involve the derivative of orde...
For the purpose of obtaining solutions to Banach-space-valued nonlinear models, we offer a new extended analysis of the local convergence result for a seventh-order iterative approach without derivatives. Existing studies have used assumptions up to...
The Sharpness-Aware Minimization (SAM) optimizer connects flatness and generalization, suggesting that loss basins with lower sharpness are correlated with better generalization. However, SAM requires manually tuning the open ball radius, which compl...
In this paper, we propose an algorithm to estimate the radius of convergence for the Picard iteration in the setting of a real Hilbert space. Numerical experiments show that the proposed algorithm provides convergence balls close to or even identical...
In this paper, we present a technique that improves the applicability of the result obtained by Cordero et al. in 2024 for solving nonlinear equations. Cordero et al. assumed the involved operator to be differentiable at least five times to extend a...
Hamming space retrieval is a hot area of research in deep hashing because it is effective for large-scale image retrieval. Existing hashing algorithms have not fully used the absolute boundary to discriminate the data inside and outside the Hamming b...
The paper solves the problem of constructing step adjustment algorithms for a gradient method based on the principle of the steepest descent. The expansion of the step adjustment principle, its formalization and parameterization led the researchers t...