2023-11

J UOZ (Volume : 12)

The study tackles the critical need for efficient optimization techniques in unconstrained optimization problems, where conventional techniques often suffer from slow and inefficient convergence. There is still a need for algorithms that strike a balance between computational efficiency and robustness, despite advancements in gradient-based techniques. This work introduces a novel conjugate gradient approach based on the logistic mapping formula. As part of the methodology, descent conditions are established, and the suggested algorithm's global convergence properties are thoroughly examined. Comprehensive numerical experiments are used for empirical validation, and the new algorithm is compared to the Polak-Ribiere (PR) algorithm. The suggested approach performs better than the PR algorithm, according to the results, and is more efficient since it needs fewer function evaluations and iterations to reach convergence. Furthermore, the usefulness of the suggested approach is demonstrated by its actual use in regression analysis, notably in the modelling of population estimates for the Kurdistan Region of Iraq. In contrast to conventional least squares techniques, the method maintains low relative error rates while producing accurate predictions. All things considered, this study presents the novel conjugate gradient approach as an effective tool for handling challenging optimization problems in both theoretical and real-world contexts.

2023-05

مجلة تكريت للعلوم الادارية والاقتصادية

دراسة

2022-03

Qalaai Zanist journal (Volume : 130)

In this paper, we talk about Fractional differential equations are generalizations of ordinary differential equations to an arbitrary (non-integer) order. Fractional differential equations have attracted considerable interest because of their ability to model complex phenomena. These equations capture nonlocal relations in space and time with power-law memory kernels. Due to the extensive applications of FDEs in engineering and science, research in this area has grown significantly all around the world. Almost the arrangement representation of fragmentary differential equation with distinctive conditions and deals with some methods for analytically solving the linear and non-linear of fractional differential equation based upon a conformable derivative by several methods and illustrate many example.In this paper, we talk about Fractional differential equations are generalizations of ordinary differential equations to an arbitrary (non-integer) order. Fractional differential equations have attracted considerable interest because of their ability to model complex phenomena. These equations capture nonlocal relations in space and time with power-law memory kernels. Due to the extensive applications of FDEs in engineering and science, research in this area has grown significantly all around the world. Almost the arrangement representation of fragmentary differential equation with distinctive conditions and deals with some methods for analytically solving the linear and non-linear of fractional differential equation based upon a conformable derivative by several methods and illustrate many example.

2021-12

Global scientific Journals (Issue : 12) (Volume : 9)

for hundreds of times, the study of probability has formerly been bandied in 1600, French mathematicians utilised probability rules to place and succeed bets. in consequence, probability proposition as sense expanded well beyond the as similar’s cross uentist academy systems of probability proposition and it's innovated on further abecedarian hypotheticals (desiderata) and is mainly further adaptable in its operations, as revealed in this job. liability proposition, in verity, is good judgement converted in to the accurate fine pronouncements in order to get introductory and extremely clear responded through the process of reduction to simulation. rather than ignoring any excellent data, difficulty is lowered to simplicity.' probability proposition as sense' simply a means for reaching constant findings in the face of inadequate moxie that extends well beyond conventional sense or deducible logic. As a result, it truly represents a sense in and itself.The fashion has a wide range of operations in a variety of scientific disciplines, including mathematics, drugs, biology, drug, economics, psychology, social lores, and numerous further. It's useful, for illustration, when logic with bitsy samples, which is typical in remedial or cerebral evaluation exploration. At the end of this paper, an illustration of such a circumstance is addressed to give a concrete case of the introductory frame. Probability knowledge has advanced extensively and is now an essential tool in statistics. The introductory theoretical generalities of probability will be addressed in this study in order to ameliorate understanding of statistical conclusion

2021-06

Turkish journal of computer and mathematics education (Volume : 12)

The Bernoulli and Riccati fractional differential equations are solved analytically using conformable derivatives in this paper. And To demonstrate the proposed solution, numerical examples of each equation are given.

2021-04

Academic Journal of Nawroz University (Volume : 10)

Two non-parametric statistical methods are studied in this work. These are the nearest neighbor regression and the Nadaraya Watson kernel smoothing technique. We have proven that under a precise circumstance, the nearest neighborhood estimator and the Nadaraya Watson smoothing produce a smoothed data with a same error level, which means they have the same performance. Another result of the paper is that nearest neighborhood estimator performs better locally, but it graphically shows a weakness point when a large data set is considered on a global scale.Two non-parametric statistical methods are studied in this work. These are the nearest neighbor regression and the Nadaraya Watson kernel smoothing technique. We have proven that under a precise circumstance, the nearest neighborhood estimator and the Nadaraya Watson smoothing produce a smoothed data with a same error level, which means they have the same performance. Another result of the paper is that nearest neighborhood estimator performs better locally, but it graphically shows a weakness point when a large data set is considered on a global scale.