w.</p><p><i>Fletcher-Reeves</i> [1]:</p><p><img src="ncg_doc_eq16009458126034669820.png" alt="$$\beta_{i+1} = \frac{g_{i+1}^T {-} g_{i+1}}{g_{i}^T g_{i}} $$" style="width:41px;height:14px;"></p><p><i>Polak-Ribiere</i> [4]:</p><p><img src="ncg_doc_eq00232388002207087152.png" alt="$$\beta_{i+1} = \frac{g_{i+1}^T (g_{i+1} {-} g_{i})}{g_{i}^T g_{i}} $$" style="width:49px;height:14px;"></p><p><i>Hestenes-Stiefel</i> [2]:</p><p><img src="ncg_doc_eq00906644648645161877.png" alt="$$\beta_{i+1} = \frac{g_{i+1}^T (g_