EXERCISE 1 Let (x) = (x + ²). (a) Show that x* = √3 is a fixed-point for p. Are there other fixed- points? (b) Write a M

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Exercise 1 Let X X A Show That X 3 Is A Fixed Point For P Are There Other Fixed Points B Write A M 1 (65.35 KiB) Viewed 32 times

EXERCISE 1 Let (x) = (x + ²). (a) Show that x* = √3 is a fixed-point for p. Are there other fixed- points? (b) Write a MATLAB function e-squareroot3(x,n) that computes the errors ekk√3 for k √3 for k = 0, 1, 2,..., n. Determine the order of the method. (Use format short e.) (c) Show that the fixed-point method using converges to √3 for any xo EI=(√3, ∞). (d) Show that the fixed-point method using converges to √3 for any To>0. (e) Show that if x > 0 then 1 Xk+1-√3: -(xk-√3)², k = 0, 1, 2,..., n. 20k Determine the order of the method. (f) Show that the fixed-point method is in fact a Newton's method in disguise. Apply Newton to f(x) = x² - 3, x > 0.