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Introduction The nonlinear conjugate gradient method (CG) is considered to solve the following unconstrained optimization problem: min f ( x ) , (1) x∈R nThe conjugate gradient(CG) method is one of the most popular and well known iterative techniques for solving sparse symmetric positive definite(SPD) systems of Conjugate Gradient Method. 1. Introduction, Notation and Basic Terms. 2. Eigenvalues and Eigenvectors. 3. The Method of Steepest Descent.