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Accelerated convergence in Newton's method for approximating square roots

Accelerated convergence in Newton's method for approximating square roots,10.1016/j.cam.2004.09.025,Journal of Computational and Applied Mathematics,M

Accelerated convergence in Newton's method for approximating square roots   (Citations: 6)
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In this paper, we construct a modification of Newton's method to accelerate the convergence of this method to the approximation of the positive square root of a positive real number. From this modification, we can define a new iterative process with prefixed order q∈N, q⩾2.
Journal: Journal of Computational and Applied Mathematics - J COMPUT APPL MATH , vol. 177, no. 1, pp. 225-229, 2005
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    • ...Also, methods based on a modification of the Newton’s method are obtained in [9]...
    • ...Finally, using combinations of basic functions identified for methods proposed in [3] and [9], new high-order methods are derived for the computation of r1/2 in [15] ...
    • ...This approach was used in [9] for the square-root computation and is extended in Section 3 to the computation of the n-th root...

    François Dubeau. Newton’s method and high-order algorithms for the nth root computation

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