Browsing by Author "Yusuph Amuda Yahaya"

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Convergence of Triple Accelerated Over-Relaxation (TAOR) Method for M-Matrix Linear Systems
(Islamic Azad University, Rasht, Iran, 2021-09-19) Khadeejah James Audu; Yusuph Amuda Yahaya; Rufus Kayode Adeboye; Usman Yusuf Abubakar
In this paper, we propose some necessary conditions for convergence of Triple Accelerated Over-Relaxation (TAOR) method with respect to 𝑀 − coefficient matrices. The theoretical approach for the proofs is analyzed through standard procedures in the literature. Some numerical experiments are performed to show the efficiency of our approach, and the results obtained compared favourably with those obtained through the existing methods in terms of spectral radius of their iteration matrices
Numerical Assessment of Some Almost Runge-Kutta and Runge-Kutta Methods for First- Order Differential Equation
(Maths Model Research Group. FUT, Minna, Nigeria, 2025-02-20) Khadeejah James Audu; Muideen Taiwo Kharashi; Yusuph Amuda Yahaya; James Nkereuwem Essien; Abraham Ajeolu Oluwasegun
Numerical methods play a critical role in solving first-order Ordinary Differential Equations (ODEs), with their efficiency and accuracy being key considerations. This study conducts a detailed comparative analysis of four numerical schemes: the Almost Runge-Kutta fourth-order scheme (ARK4), the Almost Runge-Kutta third-order fourth-stage scheme (ARK34), the classical Runge- Kutta fourth-order scheme (RK4), and the Runge-Kutta fourth-order fifth-stage scheme (RK45). The methods are evaluated based on their computational accuracy, error behavior, and efficiency. Numerical experiments reveal that all methods deliver highly accurate solutions, with ARK4 emerging as the most effective due to its lower computational complexity. ARK4 demonstrates superior performance in achieving minimal absolute error with reduced computational effort, making it a suitable choice for solving first-order ODEs. This study highlights ARK4 as a viable alternative to conventional Runge-Kutta methods for practical applications.
The Application of Linear Algebra in Machine Learning
(Paper Presentation at FUT, Minna, Nigeria, 2024-04-22) Khadeejah James Audu; Oluwatobi Oluwaseun Oluwole; Yusuph Amuda Yahaya; Samuel David Egwu
In the realm of machine learning, incorporating linear algebraic methods has become indispensable, serving as a foundational element in developing and refining various algorithms. This study explores the significant impact of linear algebra on machine learning applications, highlighting its fundamental principles and practical implications. It delves into key concepts such as vector spaces, matrices, eigenvalues, and eigenvectors, which form the mathematical basis of well-established machine learning models. The research provides a comprehensive overview of how linear algebra contributes to tasks such as classification, regression analysis, and dimensionality reduction. It also investigates how linear algebra simplifies data representation and processing, enabling effective handling of large datasets and identification of meaningful patterns. Additionally, the study explores specific machine learning applications like Word/Vector Embedding, Image Compression, and Movie Recommendation systems, demonstrating the critical role of linear algebra. Through case studies and practical examples, the study illustrates how a deep understanding of linear algebra empowers machine learning practitioners to develop robust and scalable solutions. Beyond theoretical frameworks, this research has practical implications for practitioners, researchers, and educators seeking a deeper understanding of the relationship between machine learning and linear algebra. By elucidating these connections, the study contributes to ongoing efforts to improve the efficacy and efficiency of machine learning applications.
THE PRACTICAL INTEGRATION OF LINEAR ALGEBRA IN GENETICS, CUBIC SPLINE INTERPOLATION, ELECTRIC CIRCUITS AND TRAFFIC FLOW
(Bitlis Eren University, Turkey, 2024-06-28) Khadeejah James Audu; Yak Chiben Elisha; Yusuph Amuda Yahaya; Sikirulai Abolaji Akande
A fundamental mathematical field with many applications in science and engineering is linear algebra. This paper investigates the various applications of linear algebra in the fields of traffic flow analysis, electric circuits, cubic spline interpolation, and genetics. This research delves into individual applications while emphasizing cross-disciplinary insights, fostering innovative solutions through the convergence of genetics, cubic spline interpolation, circuits, and traffic flow analysis. The research employs specific methodologies in each application area to demonstrate the practical integration of linear algebra in genetics, cubic spline interpolation, electric circuits, and traffic flow analysis. In genetics, linear algebra techniques are utilized to represent genetic data using matrices, analyze genotype distributions across generations, and identify genotype-phenotype associations. For cubic spline interpolation, linear algebra is employed to construct smooth interpolating curves, involving the derivation of equations for spline functions and the determination of coefficients using boundary conditions and continuity requirements. In electric circuit analysis, linear algebra is crucial for modeling circuit elements, formulating systems of linear equations based on Kirchhoff's laws, and solving for voltage and current distributions in circuits. In traffic flow analysis, linear algebra techniques are used to represent traffic movement in networks, formulate systems of linear equations representing traffic flow dynamics, and solve for traffic flow solutions to optimize transportation networks. By addressing contemporary challenges, emerging research frontiers, and future trajectories at the intersection of linear algebra and diverse domains, this study underscores the profound impact of mathematical tools in advancing understanding and resolving complex real-world problems across multiple fields.
Utilizing the Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations
(Malaysian Journal of Science and Advanced Technology, 2024-05-28) Khadeejah James Audu; Marshal Benjamin; Umaru Mohammed; Yusuph Amuda Yahaya
Ordinary Differential Equations (ODEs) play a crucial role in various scientific and professional domains for modeling dynamic systems and their behaviors. While traditional numerical methods are widely used for approximating ODE solutions, they often face challenges with complex or nonlinear systems, leading to high computational costs. This study aims to address these challenges by proposing an artificial neural network (ANN)- based approach for solving first-order ODEs. Through the introduction of the ANN technique and exploration of its practical applications, we conduct numerical experiments on diverse first-order ODEs to evaluate the convergence rate and computational efficiency of the ANN. Our results from comprehensive numerical tests demonstrate the efficacy of the ANN-generated responses, confirming its reliability and potential for various applications in solving first-order ODEs with improved efficiency and accuracy.
Utilizing the Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations
(Penteract Technology, Malaysia, 2024-06-16) Khadeejah James Audu; Marshal Benjamin; Umaru Mohammed; Yusuph Amuda Yahaya
Ordinary Differential Equations (ODEs) play a crucial role in various scientific and professional domains for modeling dynamic systems and their behaviors. While traditional numerical methods are widely used for approximating ODE solutions, they often face challenges with complex or nonlinear systems, leading to high computational costs. This study aims to address these challenges by proposing an artificial neural network (ANN)- based approach for solving first-order ODEs. Through the introduction of the ANN technique and exploration of its practical applications, we conduct numerical experiments on diverse first-order ODEs to evaluate the convergence rate and computational efficiency of the ANN. Our results from comprehensive numerical tests demonstrate the efficacy of the ANN-generated responses, confirming its reliability and potential for various applications in solving first-order ODEs with improved efficiency and accuracy.