Toom (surname)

Toom is a common surname in Estonia. Notable people with the surname include:

Toom

Toom may refer to:

Toom, Netherlands

Toom is a hamlet in the Dutch province of North Brabant. It is located in the municipality of Cranendonck, about 1 km west of Budel, and a few hundred metres from the Belgian border.

In the middle of the 19th century, the hamlet had a population of 140. Currently, together with neighbouring Berg, the hamlet has 340 inhabitants.

References

Coordinates: 51°16′12″N 5°33′35″E / 51.27000°N 5.55972°E / 51.27000; 5.55972

Toom–Cook multiplication

Toom–Cook, sometimes known as Toom-3, named after Andrei Toom, who introduced the new algorithm with its low complexity, and Stephen Cook, who cleaned the description of it, is a multiplication algorithm, a method of multiplying two large integers.

Given two large integers, a and b, Toom–Cook splits up a and b into k smaller parts each of length l, and performs operations on the parts. As k grows, one may combine many of the multiplication sub-operations, thus reducing the overall complexity of the algorithm. The multiplication sub-operations can then be computed recursively using Toom–Cook multiplication again, and so on. Although the terms "Toom-3" and "Toom–Cook" are sometimes incorrectly used interchangeably, Toom-3 is only a single instance of the Toom–Cook algorithm, where k = 3.

Toom-3 reduces 9 multiplications to 5, and runs in Θ(n^{log(5)/log(3)}), about Θ(n^1.465). In general, Toom-k runs in Θ(c(k) n^e), where e = log(2k − 1) / log(k), n^e is the time spent on sub-multiplications, and c is the time spent on additions and multiplication by small constants. The Karatsuba algorithm is a special case of Toom–Cook, where the number is split into two smaller ones. It reduces 4 multiplications to 3 and so operates at Θ(n^{log(3)/log(2)}), which is about Θ(n^1.585). Ordinary long multiplication is equivalent to Toom-1, with complexity Θ(n²).