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Item 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 EgwuIn 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.Item Computational Algorithm for Volterra Integral Solutions via Variational. Iterative Method(Paper Presentation at University of Lagos, Nigeria, 2023-08-28) Khadeejah James AuduThe Volterra Integral Equations (VIE) are a class of mathematical equations that find applications in various fields, including physics, engineering, and biology. Solving VIEs analytically is often challenging, and researchers have turned to numerical methods for obtaining approximate solutions. In this research, we propose a computational algorithm based on the Variational Iterative Method (VIM) to efficiently and accurately solve VIEs. By incorporating this method into the computational algorithm, we aim to improve the accuracy and convergence rate of the solutions. The performance of our algorithm was evaluated through extensive numerical experiments on various types of VIEs. The results demonstrate the effectiveness of the VIM approach in terms of accuracy, convergence rate, and computational efficiency. In conclusion, the proposed computational algorithm based on VIM presents a valuable contribution to the field of solving VIEs. It offers an efficient and accurate approach for obtaining approximate solutions, enabling researchers and practitioners to tackle complex problems that rely on VIEs. The algorithm's versatility and robustness make it a promising tool for a wide range of applications, including physics, engineering, and biology.Item Implementation of New Iterative Method for Solving Nonlinear Partial Differential Problems(Federal University, Dutsin Ma, Nigeria, 2023-11-01) Khadeejah James Audu; Stephen AmehNonlinear partial differential equations (PDEs) are prevalent in various scientific and engineering fields, demanding efficient solution methods. This study focuses on the practical application and evaluation of a well-established iterative method; New Iterative Method (NIM) for solving nonlinear PDEs. The primary aim is to assess the method's performance and applicability in solving nonlinear PDEs. We present the chosen iterative method, discuss its mathematical basis, and analyze its convergence properties, accuracy, and computational efficiency. We also provide insights into practical implementations and conduct numerical experiments on diverse nonlinear PDEs. Numerical experiments across various nonlinear PDEs confirm the method's accuracy and computational efficiency, positioning it favorably compared to existing approaches. The NIM’s versatility and computational efficiency makes it a valuable tool for tackling complex problems. This innovation has the potential to greatly benefit scientific and engineering communities dealing with nonlinear PDEs, offering a promising solution for challenging real-world problems. Keywords: Nonlinear Partial Differential Problems, Iterative Method, Computational Efficiency, Practical Implementation, Numerical ExperimentsItem Comparative Numerical Evaluation of Some Runge-Kutta Methods for Solving First Order Systems of ODEs(Toros University Publishing house, Turkey, 2025-12-12) Khadeejah James Audu; Tunde Adekunle Abubakar; Yahaya Yusuph Amuda; James Essien NkereuwemIn this study, a comparative analysis of two Runge-Kutta methods; fourth-order Runge-Kutta method and Butcher’s Fifth Order Runge-Kutta method are presented and used to solve systems of first-order linear Ordinary Differential Equations (ODEs). The main interest of this work is to test the accuracy, convergence rate and computational efficiency of these methods by using different numerical problems of ODEs. Empirical conclusions are drawn after close observation of the results presented by the two methods, which further highlights their limitations and enabling researchers to make informed decisions in choosing the appropriate technique for specific systems of ODEs problems.Item Advancements in Solving Higher-Order Ordinary Differential Equations via the Variational Iterative Method.(Akdeniz University, Turkey, 2025-12-30) Khadeejah James Audu; Michael Ogbole Ogwuche; Sıkırulaı Abolaji Akande; Yahaya Yusuph AmudaThis study presents advancements in solving higher-order ordinary differential equations (ODEs) using the Variational Iterative Method (VIM) and compares its performance with the New Iteration Method (NIM) and Adomian Decomposition Method (ADM). ODEs are critical in modeling the rate of change in various systems over time, and many do not have exact solutions, necessitating the use of numerical methods to obtain approximate results. While several iterative methods exist, a detailed comparison of VIM with other techniques, particularly for higher-order ODEs, is still lacking. This research focuses on understanding the principles and methodology of VIM and applying it to solve higher-order linear and nonlinear ODEs. The study evaluates the accuracy, convergence rate, and computational efficiency of VIM compared to NIM and ADM through the solution of third, fourth, and fifth-order differential problems. The results show that VIM outperforms NIM and ADM, with faster convergence and higher efficiency. Error analysis in Figures 1, 2, and 3 highlights the strengths and limitations of each method, providing valuable insights for researchers and practitioners in selecting the most appropriate technique for solving higher-order ODEs. These findings advance the development of iterative methods in numerical analysis and contribute to progress in the field of differential equations.Item Application of Hidden Markov Model in Yam Yield Forecasting.(African Journal Online (AJOL), Soutrh Africa, 2022-06-06) 11. Lawal Adamu; Saidu Daudu Yakubu; Didigwu Ndidiamaka Edith; Abdullahi Abubakar; Khadeejah James Audu; Isaac Adaji.Providing the government and farmers with reliable and dependable information about crop yields before each growing season begins is the thrust of this research. A four-state stochastic model was formulated using the principle of Markov, each state of the model has three possible observations. The model is designed to make a forecast of yam yield in the next and subsequent growing seasons given the yam yield in the present growing season. The parameters of the model were estimated from the yam yield data of Niger state, Nigeria for the period of sixteen years(2001-2016). After which, the model was trained using Baum-Welch algorithm to attend maximum likelihood. A short time validity test conduct on the model showed good performance. Both the validity test and the future forecast shows prevalence of High yam yield, this attest to the reality on the ground, that Niger State is one of the largest producers of yam in Nigeria. The general performance of the model, showed that it is reliable therefore, the results from the model could serve as a guide to the yam farmers and the government to plan strategies for high yam production in the region.Item Assessment of Numerical Performance of Some Runge-Kutta Methods and New Iteration Method on First Order Differential Problems(Federal University, Dutse, Nigeria, 2023-12-10) Khadeejah James Audu; Aliyu Rasheed Taiwo; Abdulganiyu Alabi SoliuThis research focuses on the assessment of the numerical performance of some Runge-Kutta methods and New Iteration Method “NIM” for solving first-order differential problems. The assessment is conducted through extensive numerical experiments and comparative analyses. Accuracy, efficiency, and stability are among the key factors considered in evaluating the performance of the methods. A range of first-order differential problems with diverse characteristics and complexity levels is employed to thoroughly examine the methods' capabilities and limitations. The numerical investigation that is defined in the study as well as the results that are stated in the Tables, demonstrates that all the approaches produce extremely accurate results. However, the “NIM” was shown to be the most effective of the three methods used in this study. Conclusively, the “NIM” should be employed to solve first-order nonlinear and linear ordinary differential equations in place of Runge-Kutta Fourth order method (RK4M) and Butcher Runge-Kutta Fifth order method (BRK5M). In addition, BRK5M is more applicable and efficient than RK4M when solving first order ordinary differential problems.Item BLOCK METHOD APPROACH FOR COMPUTATION OF ERRORS OF SOME ADAMS CLASS OF METHODS(Association of Nigerian Journal of Physics, 2022-12-12) Yahaya, Y. A.; Odeyemi, A. O.; Khadeejah James AuduTraditionally, the error and order constant of block linear multistep methods were analyzed by examining each block members separately. This paper proposes a block-by-block analysis of the schemes as they appear for implementation. Specifically, cases when k= 2, 3, 4, and 5 for Adams Moulton (implicit) are reformulated as continuous schemes in order to generate a sufficient number of schemes required for the methods to be self-starting. The derivation was accomplished through the continuous collocation technique utilizing power series as the basis function, and the property of order and error constants is examined across the entire block for each case of the considered step number. The findings of the study generated error constants in block form for Adams Bashforth and Adams Moulton procedures at steps 2, 3, 4, 5 k . Furthermore, the relevance of the study demonstrates that calculating all members' error constants at once, reduces the amount of time necessary to run the analysis. The new approach, for examining the order and error constants of a block linear multistep method, is highly recommended for application in solving real-world problems, modelled as ordinary and partial differential equationsItem A THIRD REFINEMENT OF JACOBI METHOD FOR SOLUTIONS TO SYSTEM OF LINEAR EQUATIONS(Federal University, Dutsin Ma, Nigeria, 2023-10-15) Khadeejah James Audu; James Nkereuwem Essien; Abraham Baba Zhiri; Aliyu Rasheed TaiwoSolving linear systems of equations stands as one of the fundamental challenges in linear algebra, given their prevalence across various fields. The demand for an efficient and rapid method capable of addressing diverse linear systems remains evident. In scenarios involving large and sparse systems, iterative techniques come into play to deliver solutions. This research paper contributes by introducing a refinement to the existing Jacobi method, referred to as the "Third Refinement of Jacobi Method." This novel iterative approach exhibits its validity when applied to coefficient matrices exhibiting characteristics such as symmetry, positive definiteness, strict diagonal dominance, and 𝑀 -matrix properties. Importantly, the proposed method significantly reduces the spectral radius, thereby curtailing the number of iterations and substantially enhancing the rate of convergence. Numerical experiments were conducted to assess its performance against the original Jacobi method, the second refinement of Jacobi, and the Gauss-Seidel method. The outcomes underscore the "Third Refinement of Jacobi" method's potential to enhance the efficiency of linear system solving, thereby making it a valuable addition to the toolkit of numerical methodologies in scientific and engineering domains.Item 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 AkandeA 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.