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or a tolerance for how "bad" our final iterate is allowed to be. One way to set this "badness" tolerance is to use the magnitude |dk . This magnitude measures how well xk solves the linear system. So if e is our prescribed tolerance (could be relatively large for a hard problem or as small as machine epsilon when you need to be precise), then the algorithm for the method of steepest descent can be described as follows: Prescribe a tolerance e. Start with any initial iterate xo. Compute (1) dk-1 = -(AXk-1 - b), Ildk-1/12 (2) tk-1 - dk-1 . (Adk-1) (3) XK = Xk-1 + t*-1 dk-1. Compute Ildkl|. If | |dkl| 2 6, repeat computations (1)-(3) for the next iterate. Else if Ildkl|