Abstract

THE CONCEPTS OF CONVERGENCE OF CONJUGATE GRADIENT METHOD OF QUADRATIC FUNCTIONAL

Adamu Wakili

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Abstract The conjugate gradient method is one of the most popular technique for solving symmetric and positive definite system of linear equations. The study of optimization theory using Chebyshev polynomials showed that conjugate gradient method converges at certain boundary values. This method is most effective for finding a minimizer of a smooth non-linear function when second derivatives are either not available or difficult to evaluate. Line Search and Quadratic functions are used to test for convergent of the function which is symmetric and positive definite. The conjugate gradient method showed that the function converges at certain values ( eigen values) of the symmetric matrix. Key words: Conjugate Gradient Method, symmetric, positive definite and functional.

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