Conjugate Gradient Method And Its Extensions

In this project we investigate conjugate gradient method and its extension to solve unconstrainedrnminimization problems. There are two important methods for solving linear equationsrnand nonlinear optimization problems. The performance of the linear conjugate gradientrnmethod is tied to the distribution of the eigenvalues of the coe cient matrix. Nonlinear conjugaterngradient method is used for solving large-scale nonlinear optimization problems andrnhas wide applications in many elds. It is also discussed how to use the result to obtain thernconvergence of the famous Fletcher-Reeves, and Polak-Ribiere conjugate gradient methods.rnAnd comparisons are made among the algorithms of the steepest descent method, Newton'srnmethod and conjugate gradient method for quadratic and nonquadratic problems.

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