论文信息 - The Middle Product Algorithm I

The Middle Product Algorithm I

Abstract.We present new algorithms for the inverse, division, and square root of power series. The key trick is a new algorithm – MiddleProduct or, for short, MP – computing the n middle coefficients of a (2n−1)×n full product in the same number of multiplications as a full n×n product. This improves previous work of Brent, Mulders, Karp and Markstein, Burnikel and Ziegler. These results apply both to series and polynomials.

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