Faster algorithms for the square root and reciprocal of power series

We give new algorithms for the computation of square roots and reciprocals of power series in CJxK. 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).