Space- and Time-Efficient Polynomial Multiplication

被引：0

作者：

Roche, Daniel S. ^{[1
]}

机构：

[1] Univ Waterloo, Cheriton Sch Comp Sci, Waterloo, ON N2L 3G1, Canada

来源：

ISSAC2009: PROCEEDINGS OF THE 2009 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION | 2009年

关键词：

Polynomial multiplication; integer multiplication; space efficiency; time-space tradeoff;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Countless algorithms have been developed for the multiplication of univariate polynomials and multi-precision integers, but all those with sub-quadratic time complexity currently require at least Omega(n) extra space for the computation. A new routine based on the Karatsuba/Ofman algorithm is presented with the same time complexity of O(n(1.59)) but only O(log n) extra space. A second routine based on the method of Schonhage/Strassen achieves the same pseudo-linear time and O(1) extra space, but only under certain conditions. A preliminary implementation over F(p)[x], where p fits into a single machine word, is presented and compared with existing software.

引用

页码：295 / 301

页数：7

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