MATLAB Implementation of the Conjugate Gradient Method

This article discusses our implementation of the conjugate gradient method for computing optimal solutions through programming. The implementation utilizes MATLAB, and we provide both the code and supporting documentation. During the development process, we employed various techniques and methodologies to ensure program correctness and efficiency, incorporating key algorithmic components such as gradient computation, direction vector updates, and step size optimization. We conducted extensive testing and debugging to validate proper program execution and guarantee convergence to optimal solutions. Our approach involved thorough research of relevant literature to ensure we adopted the most advanced and suitable methodology for our specific problem domain. Through this implementation, we gained deeper insights into the conjugate gradient algorithm's computational mechanics, enabling faster and more accurate determination of optimal solutions. The code structure includes functions for initializing parameters, calculating residuals, updating search directions using orthogonal conjugate vectors, and implementing convergence criteria checks.