Third Order Convergence for Square Roots Using Newton's Method

[ijabbott]

(08-27-2019 06:32 PM)Namir Wrote:  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 + A)
where X(0) is the initial guess for the square root of N.

Quote:Given N and X (initial guess) and tolerance toler:

Code:


Repeat
  Y = X*X;
  X = X * (Y + 3*N) / (3*Y + A)
Until Abs(X*X-A) <= toler

Hi Namir,

Could you clarify what variable A is used for? Thanks!