Fast Computation of the n-th Root in Quad-double Arithmetic Using a Fourth-order Iterative Scheme

Abstract

We propose new algorithms for computing the n-th root of a quad-double number. We construct an iterative scheme that has quartic convergence and propose algorithms that require only about 50% to 60% of the double-precision arithmetic operations of the existing algorithms. The proposed algorithms perform about 1.7 times faster than the existing algorithms, yet maintain the same accuracy. They are sufficiently effective and efficient to replace the existing algorithms.