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Algorithm Steps

The steps of Broyden’s algorithm (Good Method) are as follows:

  1. Initialize \mathbf{x}_0 and \mathbf{B}_0 (e.g., \mathbf{B}_0 = \mathbf{I} , the identity matrix).
  2. For k = 0, 1, 2, \dots :
\mathbf{B}_{k+1} = \mathbf{B}_k + \frac{(\mathbf{y}_k - \mathbf{B}_k \mathbf{s}_k) \mathbf{s}_k^\top}{\mathbf{s}_k^\top \mathbf{s}_k}.