1. Solve the following nonlinear system by the Newton method. f(x, y, z) = xyz - 1 = 0 g(x, y, z) 22 + y XXXXXXXXXX = 0 h(x, y, z) x2 + 2 y? 3 = 0 Use as initial guess, x=1.0, y = 1.2, z = 1.4. At...

1. Solve the following nonlinear system by the Newton method. f(x, y, z) = xyz - 1 = 0 g(x, y, z) 22 + y2 + 22 - 4 = 0 h(x, y, z) x2 + 2 y? 3 = 0 Use as initial guess, x=1.0, y = 1.2, z = 1.4. At each iteration Xk+1 X* - J-'F(XK) you need to solve linear system JAX = F(X) (1) , rather than forming the inverse of the Jacobian. To solve the linear system download the dgefa.f and dgesl.f from linpack in www.netlib.org. Also, they have dependencies, like daxpy, dscal and idamax, etc, from BLAS, also in lin- pack. But keep in mind that they are f77 routines, so you have to convert them into f90 routines. (Probably the only thing you need to do is to change the 'c' comment character into '!' in f90.) Iterate until X* ||/ || X(k+1)||