Numerical methods for solving the system of nonlinear equations

Q1[5+5+5 pts]. Consider numerical methods for solving the system of nonlinear equations
xl + xi x2 XiX3 + 6 = 0, exi + ex2 = x3, x?- 2x1x3 = 4,
T where x(1) = (—v+i•-2, v+1)
a. Describe one iteration of the Newton method. Then use the method to approximate a solution of the system and stop the iteration when
either I jx(k+1) — x(k) I I co < 10-5 or the number of iterations reaches 100.
If the method successes to solve the problem, state the solution x* and give the required number of iterations. Otherwise, if the method fails to solve the problem, give a reason for the failure. b. Redo the previous question, but by applying the steepest descent method to a certain minimization problem. c. Redo the latter question, but by applying either the DFP or BFGS method.

Sample Solution

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