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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 Application of Grey-Markov Model for Forecasting Nigeria Annual Rice Production(African Journal Online (AJOL), South Africa, 2021-11-21) Lawal Adamu; Didigwu, N. E.; Saidu, D. Y; Sadiq, S. L.; Khadeejah James AuduIn this paper, Grey system model (GM(1,1)) and Grey-Markov model that forecast Nigeria annual Rice production have been presented. The data used in the research were collected from the archive of Central Bank of Nigeria for a period of Six years (2010-2015). The fitted models showed high level of accuracy. Hence, the models can be used for food security plans of the nation.Item 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 AbubakarIn 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 matricesItem A Backward Diffrention Formula For Third-Order Inttial or Boundary Values Problems Using Collocation Method(Islamic Azad University,Rasht ', Iran, 2021-09-19) AbdGafar Tunde Tiamiyu; Abosede Temilade Cole; Khadeejah James AuduWe propose a new self-starting sixth-order hybrid block linear multistep method using backward differentiation formula for direct solution of third-order differential equations with either initial conditions or boundary conditions. The method used collocation and interpolation techniques with three off-step points and five-step points, choosing power series as the basis function. The convergence of the method is established, and three numerical experiments of initial and boundary value problems are used to demonstrate the efficiency of the proposed method. The numerical results in Tables and Figures show the efficiency of the method. Furthermore, the numerical method outperformed the results from existing literature in terms of accuracy as evident in the results of absolute errors producedItem 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.