6.6 Powell’s Method 325ll llllll lFigure 6.9 Flowchart for Powell’s Method.direction are points that are minima alongSnin the first cycle, the first pattern direction
S(p^1 )in the second cycle, the second pattern directionS(p^2 )in the third cycle, and so on.
Quadratic Convergence. It can be seen from Fig. 6.9 that the pattern direc-
tionsSp(^1 ),S(p^2 ),S(p^3 ),... are nothing but the lines joining the minima found along
the directions Sn,S(p^1 ),S(p^2 ),... ,respectively. Hence by Theorem 6.1, the pairs of
directions(Sn,Sp(^1 )),(S(p^1 ),S(p^2 )), nd so on, area A-conjugate. Thus all the directions