Article ID Journal Published Year Pages File Type
4641760 Journal of Computational and Applied Mathematics 2009 11 Pages PDF
Abstract

Two modifications of Newton’s method to accelerate the convergence of the nnth root computation of a strictly positive real number are revisited. Both modifications lead to methods with prefixed order of convergence p∈N,p≥2p∈N,p≥2. We consider affine combinations of the two modified ppth-order methods which lead to a family of methods of order pp with arbitrarily small asymptotic constants. Moreover the methods are of order p+1p+1 for some specific values of a parameter. Then we consider affine combinations of the three methods of order p+1p+1 to get methods of order p+1p+1 again with arbitrarily small asymptotic constants. The methods can be of order p+2p+2 with arbitrarily small asymptotic constants, and also of order p+3p+3 for some specific values of the parameters of the affine combination. It is shown that infinitely many ppth-order methods exist for the nnth root computation of a strictly positive real number for any p≥3p≥3.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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