Solve the following system of nonlinear equations using Newt

Solve the following system of non-linear equations using Newton\'s Method and fixed point iteration (35%) x^2 + 2x + 2y^2 - 26 = 0 2x^3-y^2 + 4y- 19 = 0 Start at x= 1.0, y = 1.0. Carry out the first five iterations for both cases

Solution

Suppose that Pk has been obtained. Step 1. Evaluate the function F(Pk ) = f1(pk , qk ) f2(pk , qk ) . Step 2. Evaluate the Jacobian J(Pk ) = x f1(pk , qk ) y f1(pk , qk ) x f2(pk , qk ) y f2(pk , qk ) . Step 3. Solve the linear system J(Pk )P = F(Pk ) for P. Step 4. Compute the next point: Pk+1 = Pk + P. Now, repeat the process.