Question: Using Bisection Method 2. (Gu Spring 2012 Sample Midterm #1) moved (a) Show that the cubic equation 2x3 - 6x + 1 = 0 has

Using Bisection Method

2. (Gu Spring 2012 Sample Midterm #1) moved (a) Show that the cubic equation 2x3 - 6x + 1 = 0 has a real root in the interval [0, 1/2]. Perform one step of the bisection method with this interval. (b) Reformulate the above equation as 2x3 + 1 6 Define the fixed point iteration (FPI) based on this equation, and show that FPI converges for any initial guess in [0, 1/2]

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