Third Order Convergence for Square Roots Using Newton's Method

08272019, 06:32 PM
(This post was last modified: 08282019 01:41 AM by Namir.)
Post: #1




Third Order Convergence for Square Roots Using Newton's Method
Hi All,
Most of us are familiar with the second order converging algorithm for obtaining the square root of N: X(n+1) = (X(n) + N/X(n)) / 2 where X(0) is the initial guess for the square root of N. I stumbled on a third order converging algorithm in an book about ODEs and PDEs. The algorithm is: X(n+1) = X(n)*(X(n)^2 + 3*N)(3*X(n)^2 + N) where X(0) is the initial guess for the square root of N. I compared the two algorithms using Excel and the second one does converge faster than the first one. The pseudocode for the second algorithm is: Given N and X (initial guess) and tolerance toler: Code:
Enjoy! Namir 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)