QUICKEST DESCENT. 9 



Therefore, by substituting for y«, and i«, iu 

 equation (1), and by transposition, 



P* p2 p* 



» 



C < ■- , - 4- 6p*x« 4- p3a?« 1:^ — s-^ 



P* P' ^ ^ ^ P^ 



p« 



Let ir = p+Ap« +Bp3^Cp4-|-Dp5; then, 



— x* = — p4 — 4Ap» — (6A2+4B)p« 



— (12AB + 4A3 4-4C)p7 



— (A4+ 12A« B4.12AC + 6B24-4D)p8. 



— 2p»a^ = — 2p« — 6Ap« 



— (6A2 + 6B)p7— (12 AB + 6C4.2A3)p8. 



— -?^i^= — 4p4 — 20 Ap5 — (36A2 + 24B) p« 



P2 



—(28 A3 4- 84AB + 28 C)p'— 



— (8 A4 4-96 A2B4 96 AC + 48 B^ 432 D) ps . 



^tSPf= _8p^ ^32Ap» 



P* 



— (40A*4-40B)p^ 



— (16 A» 4-96 A 84-48 C) p» . 

 B 



