Recall the nonlinear system in Problem 101:

a. Locate the roots graphically.

b. Based on the location of the roots, select suitable auxiliary functions g1 and g2 and apply the fixed-point iteration method with (−1, −2) as the initial estimate, ε = 10−4, and number of iterations not to exceed 20, to find one of the two roots.

c. To find the other root, write the original equations in reverse order, suitably select g1 and g2, and apply fixed-point iteration with all information as in (b).

Problem 101

Consider the nonlinear system

a. Solve using Newton’s method with initial estimate (−1, −2), tolerance ε = 10−4, and a maximum of 10 iterations.

b. Repeat (a) but with an initial estimate (−2, 0).

c. Use a graphical approach to validate the results in (a) and (b).

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