Search results
Results from the WOW.Com Content Network
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.
Splitting numbers into more than two parts results in Toom-Cook multiplication; for example, using three parts results in the Toom-3 algorithm. Using many parts can set the exponent arbitrarily close to 1, but the constant factor also grows, making it impractical.
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
In binary (base-2) math, multiplication by a power of 2 is merely a register shift operation. Thus, multiplying by 2 is calculated in base-2 by an arithmetic shift. The factor (2 −1) is a right arithmetic shift, a (0) results in no operation (since 2 0 = 1 is the multiplicative identity element), and a (2 1) results in a left arithmetic shift ...
By the commutative law, the middle two terms cancel: = leaving (+) = The resulting identity is one of the most commonly used in mathematics. Among many uses, it gives a simple proof of the AM–GM inequality in two variables. The proof holds in any commutative ring.
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.
The Karatsuba algorithm is equivalent to Toom-2, where the number is split into two smaller ones. It reduces four multiplications to three and so operates at Θ(n log(3)/log(2)) ≈ Θ(n 1.58). Although the exponent e can be set arbitrarily close to 1 by increasing k, the constant term in the function grows very rapidly.