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A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the t
The classical method of multiplying two n-digit numbers requires n 2 digit multiplications. Multiplication algorithms have been designed that reduce the computation time considerably when multiplying large numbers. Methods based on the discrete Fourier transform reduce the computational complexity to O(n log n log log n).
Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.
The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. This is achieved by noting that the final digit is completely determined by multiplying the last digit of the multiplicands. This is held as a temporary result.
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]
With the chisanbop method it is possible to represent all numbers from 0 to 99 with the hands, rather than the usual 0 to 10, and to perform the addition, subtraction, multiplication and division of numbers. [4] The system has been described as being easier to use than a physical abacus for students with visual impairments. [5]
The method was based on lattice multiplication, and also called rabdology, a word invented by Napier. Napier published his version in 1617. [1] It was printed in Edinburgh and dedicated to his patron Alexander Seton. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to ...
The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school, this algorithm is sometimes called the grammar school method. [1]
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