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I am now reading an image processing paper, which uses scale congjugate gradient algorithm to minimize a linear system object function. This paper is the first one that proposes the idea of scale congjugate gradient algorithm. After reading the paper, I am still unclear what makes scale conjgugate gradient method a good candidate for optimization. I understand that conjugate gradient method is a better optimization method compared to the gradient descent method because it can converge much first. But it is based on the assumption that the linear system is symmetric and positive-define. It seems to me that scale congjugate gradient algorithm does not have this limitation if I understand well about the paper. So my question is in which condition we can use scale congjugate gradient method rather than the conjugate gradient method or the gradient descent method. Thanks.

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