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The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [ 1 ] [ 2 ] [ 3 ] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most n log 2 3 ...
He is the main developer of GNU TeXmacs (a free scientific editing platform) [3] and Mathemagix (free software, a computer algebra and analysis system). [ 4 ] In 2019, van der Hoeven and his coauthor David Harvey announced their discovery of the fastest known multiplication algorithm , allowing the multiplication of n {\displaystyle n} -bit ...
When done by hand, this may also be reframed as grid method multiplication or lattice multiplication. In software, this may be called "shift and add" due to bitshifts and addition being the only two operations needed. In 1960, Anatoly Karatsuba discovered Karatsuba multiplication, unleashing a flood of research into fast multiplication ...
As making the partial products is () and the final addition is (), the total multiplication is (), not much slower than addition. From a complexity theoretic perspective, the Wallace tree algorithm puts multiplication in the class NC 1. The downside of the Wallace tree, compared to naive addition of partial products, is its much higher ...
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007. It is asymptotically faster than older methods such as Karatsuba and Toom–Cook multiplication , and starts to outperform them in practice for numbers beyond about 10,000 to 100,000 decimal digits. [ 2 ]
This category contains articles pertaining to algorithms that are used in arbitrary-precision arithmetic. This includes algorithms for multiplication and division , as well as algorithms for the efficient evaluation of mathematical constants and special functions to high precision.
In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the fastest algorithm for matrix multiplication is of major practical ...