I've been studying Conjugate Gradient method. Before the method is explained, the book starts with the definition of a scalar, quadratic function of a vector like the below.
$$f(x) = \frac{1}{2}x^TAx - b^Tx+c \quad \quad \text{where A : matrix, b: vector, c : scalar}$$
Then, the book said f(x) is minimized by the solution to $Ax=b$.
However, I don't understand why the author defines the function in the way above, and what's the meaning of the function. Is there any
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alryosha
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It is an algebraic expression for what is usually known as energy functional. – Algebraic Pavel Oct 24 '19 at 16:28
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Is there any material that I can acquire the knowledge of the quadratic function? – alryosha Oct 30 '19 at 03:50