Page 215 - Applied Numerical Methods Using MATLAB

204 NONLINEAR EQUATIONS
Table P4.7 Applying newtons()/fsolve() for Systems of Nonlinear Equations
newtons() fsolve()
x 0 = [1 0.5] x
(P4.7.1) ||f(x)||
Flops 1043 1393
x 0 = [1 0.5] x [0.1560 0.4111]
(P4.7.2) ||f(x)|| 3.97e-15 (3.66e-15)
Flops 2489 3028
x 0 = [1 0.5] x
(P4.7.3) ||f(x)||
Flops 1476 3821
x 0 = [1 0.5] x [0.5024 0.1506]
(P4.7.4) ||f(x)|| 8.88e-16 (1.18e-6)
Flops 1127 1932
x 0 = [1 0.5] x
(P4.7.5) ||f(x)||
Flops 2884 3153
x 0 = [1 0.5] x [1.6922 -1.6408]
(P4.7.6) ||f(x)|| 1.83e-15
Flops 9234 12896
x 0 = [1 0.5] x
(P4.7.7) ||f(x)||
Flops 2125 2378

x 0 = [1 0.5] x [0.2321 1.5067]
(P4.7.8) ||f(x)|| 1.07 (1.07)
Flops 6516 6492
x 0 = [1 0.5] x
(P4.7.9) ||f(x)||
Flops 1521 1680
x 0 = [1 0.5] x [0.2236 0.1273]
(P4.7.10) ||f(x)|| 0 (1.11e-16)
Flops 1278 2566
(cf) The numbers of floating-point operations and the residual (mismatching) errors in the parentheses are obtained
from MATLAB 5.x version.