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arXiv · 0910.1926

Faster algorithms for the square root and reciprocal of power series

David Harvey
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Abstract

We give new algorithms for the computation of square roots and reciprocals of power series in C[[x]]. If M(n) denotes the cost of multiplying polynomials of degree n, the square root to order n costs (1.333... + o(1)) M(n) and the reciprocal costs (1.444... + o(1)) M(n). These improve on the previous best results, respectively (1.8333... + o(1)) M(n) and (1.5 + o(1)) M(n).

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David Harvey. 2009-10-10. Faster algorithms for the square root and reciprocal of power series. https://arxiv.org/abs/0910.1926

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