Flattening Karatsuba’s Recursion Tree into a Single Summation

Autor: Baruchel, Thomas
Zdroj: SN Computer Science; January 2020, Vol. 1 Issue: 1
Abstrakt: The recursion tree resulting from Karatsuba’s formula is built here using an interleaved splitting scheme rather than the traditional left/right one. This allows an easier access to the nodes of the tree and some of them are initially flattened all at once into a single recursive formula. The whole tree is then flattened further into a convolution formula involving less elementary multiplications than the usual Cauchy product—leading to iterative (rather than recursive) implementations of the algorithm. Unlike the traditional splitting scheme, the interleaved approach may also be applied to infinite power series, and the corresponding formulas are also given.
Databáze: Supplemental Index
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