Faster algorithms for the square root and reciprocal of power series

Details Faster algorithms for the square root and reciprocal of power series Faster algorithms for the square root and reciprocal of power series

2009-10-10

arxiv.org/abs/0910.1926v1

Computer Science

Symbolic Computation

6 pages, 1 figure, requires algorithm2e package

Scientific paper

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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