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Conjugate gradient method

We can also compute the residual iteratively as ˆrk+1=ˆbˆAˆxk+1, which equals ˆbˆA(ˆxk+αkˆpk), or (ˆbˆAˆxk)αkˆAˆpk, which gives ˆrk+1=ˆrkˆAˆpk,