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I am using Linear Conjugate Gradient to solve for $x$ in $Ax=b$, where $A$ is PSD. I noticed experimentally that the Rayleigh Quotient $\frac{x_k^TAx_k}{x^Tx}$ of the accumulated solution $x_k$ is always monotonically decreasing with more iterations. This obsevation seems nontrivial to me and I wonder if it is theoretically guaranteed that this is true.

HANDSOMEJACKANDY
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  • Please define your problem. You tagged the question [tag:linear-algebra]. Does that imply it's a linear problem that you're solving with conjugate gradients? – joriki Mar 15 '23 at 04:37
  • Thank you for your advice. Just adjusted the wording of the problem. – HANDSOMEJACKANDY Mar 15 '23 at 23:49

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