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The CG conjugate gradient method is an iterative method used to solve matrix equations. It was first introduced by Hhestens and Stiefel. The method utilizes conjugate directions to efficiently solve the problem by minimizing the error between the approximate solution and the true solution. This algorithm has been widely used in various fields, including computer graphics, numerical optimization, and scientific computing. The CG method has proven to be highly effective, providing a significant improvement in speed and accuracy compared to other methods. Furthermore, the method can be adapted to solve a wide range of problems, making it a versatile tool in scientific research and engineering.