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Third Order Convergence for Square Roots Using Newton's Method
08-27-2019, 07:49 PM
Post: #2
RE: Third Order Convergence for Square Roots Using Newton's Method
(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!

— Ian Abbott
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RE: Third Order Convergence for Square Roots Using Newton's Method - ijabbott - 08-27-2019 07:49 PM



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