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I am using gradient descent to solve the linear system $Ax=b$, where matrix $A$ is symmetric and positive definite. More precisely, I am attempting to solve the following quadratic program

$$\text{minimize} \quad \frac{1}{2}x^TAx-b^Tx$$

A logarithmic plot of the residual norms ($\rho_k$) after $K$ steps forms a straight line sloping down to the right. I was asked to produce a least-squares approximation to $\log(\rho_k)$ where $k \in \{K, \dots, N\}$ in order to determine $\beta$ and $\gamma$ where

$$\log(\rho_k) \approx \beta + \gamma(k-K)$$

and am not sure what to do. Any help would be appreciated.

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  • $\begingroup$ Is $K$ the dimension of $A$? $\endgroup$ – LutzL Apr 26 at 19:14
  • $\begingroup$ Using uppercase for both matrices and integers is a huge turnoff. $\endgroup$ – Rodrigo de Azevedo Apr 27 at 16:15
  • $\begingroup$ Take the part of the curve that looks linear and use least-squares. $\endgroup$ – Rodrigo de Azevedo Apr 27 at 16:19

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