81 nonlinear equations case 1. 0s0<45° or 0s #'(x)<1 case 2. 45°0<90° or (x) 21 monotonously convergent sequence monotonously divergent sequence ')21 45 0< 90°

81 Nonlinear Equations Case 1. 0S0<45° or 0s #'(x)<1 Case 2. 45°0<90° or (x) 21 Monotonously Convergent Sequence Monotonously Divergent Sequence ')21 45 0< 90° 0s o(x)<1 00<45 Y=x y=x Case 3. 90°s 0S135° or #'(x) S-1 Case 4. 135°<0< 180 or -1<0(x) <0 Oscillatory Divergent Sequence Oscillatory Convergent Sequence y=x yX $)-1 90 0 135 -1<¢'x) s 0 1350< 180° y=px) y p(x) Fig. 3.16 Geometrical representations of convergence conditions of Fixed-Point method