Browsing by Author "Tibebu, Zewdie"

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    Conjugate Gradient Method and its Extensions
    (Addis Ababa University, 2018-05-01) Tibebu, Zewdie; Guta, Berhanu (PhD)
    In this project we investigate conjugate gradient method and its extension to solve unconstrained minimization problems. There are two important methods for solving linear equations and nonlinear optimization problems. The performance of the linear conjugate gradient method is tied to the distribution of the eigenvalues of the coe cient matrix. Nonlinear conjugate gradient method is used for solving large-scale nonlinear optimization problems and has wide applications in many elds. It is also discussed how to use the result to obtain the convergence of the famous Fletcher-Reeves, and Polak-Ribiere conjugate gradient methods. And comparisons are made among the algorithms of the steepest descent method, Newton's method and conjugate gradient method for quadratic and nonquadratic problems.