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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 single-digit ...
Trachtenberg defined this algorithm with a kind of pairwise multiplication where two digits are multiplied by one digit, essentially only keeping the middle digit of the result. By performing the above algorithm with this pairwise multiplication, even fewer temporary results need to be held.
To multiply two numbers with n digits using this method, one needs about n2 operations. More formally, multiplying two n -digit numbers using long multiplication requires Θ ( n2) single-digit operations (additions and multiplications).
Elementary arithmetic. The symbols for elementary-level math operations. From top-left going clockwise: addition, division, multiplication, and subtraction. Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position ...
Lattice multiplication. Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, [1] sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers. It is mathematically identical to the more commonly ...
Multiplication (often denoted by the cross symbol Ă—, by the mid-line dot operator â‹…, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division.
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