The square root of c, for c > 0. can be found by iterating the expression where

Question

The square root of c, for c > 0. can be found by iterating the expression where xo > 0. Find using the above expression. Derive the above expression (note, there are multiple ways to do this).

Explanation / Answer

(a) Just put c = 2 and use the following pseudocode x = 1 while( abs(x^2-2)>0.0001) x = 0.5 (x + 2/x) end (b) Apply newton's method to the equation f(x) = x^2 - c. Newton's method says that x(n+1) = x(n) - f(x(n))/f'(x(n)) In this case, note that f(x(n)) = x(n)^2 - c and f'(x(n)) = 2 x(n) Substitute and simplify x(n+1) = x(n) - [x(n)^2 - c]/[2 x(n)] = [2 x(n)^2 - x(n)^2 + c]/[2 x(n)] = [x(n) + c/x(n)]/2

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.