1-12 Multiplication Chart
1-12 Multiplication Chart 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 2 6 8 10 12 14 16 18 20 22 24 3 6 12 15 18 21 24 27 30 33 36
Integer Multiplication
Q Is it possible to do with fewer multiplications? A Yes [Gauss] x = ac - bd, y = (a + b) (c + d) - ac - bd Remark Improvement if no hardware multiply 4 multiplications, 2 additions 3 multiplications, 5 additions Integer Multiplication Section 5 5
Matrix Multiplication - Baylor ECS
n Multiplications: M(n) = 8M(n/2), M(1)=8 n Additions: A(n) = 8A(n/2)+n 2 n M(n) = 8 lg n = n lg 8 = n 3 n Additions are also Θ(n 3), but point is moot n Can we reduce the 8 multiplications in the base equations
Flashcards - 0 - multiplication
11 Flashcards www Multiplication com 3 x 11 3333 www multiplication com 2 x 11 2222 www multiplication com 1111 x x x 111111 1111 www multiplication com
SPRING 2004 Ultra-Fast Matrix Multiplication
scalar multiplications as opposed to the usual eight Even though it has been shown that Strassen’s algorithm is opti-mal for two-by-two matrices [6], there have been asymptotic improvements to the algorithm for very large matrices Thus, the search for improvements over Strassen’s algorithm for smaller matrices is still being conducted Even
ALGORITHMS FOR MATRIX MULT~~WATION BY R P BRENT
multiplications and n - 1 additions Hence, the m p elements cik can be found in mnp multiplications and m(n - 1)p additions, and about the same number of loads, stores and address computations If we count only multiplications
By Alan Walker Illustrated by Jesus Murillo
Memorize in Minutes: The Times Tables Student Manual The 0's and 1's multiplication facts are really easy 0’s Any number times 0 is always zero
Matrix multiplication based graph algorithms
Matrix multiplication algorithms - Recent developments Complexity Authors n2 376 Coppersmith-Winograd (1990) n2 374 Stothers (2010) n2 3729 Williams (2011) n2 37287 Le Gall (2014)
Homework 2
(a)Show that ve multiplications are su cient to compute the square of a 2 2 matrix (b)What is wrong the the following algorithm for computing the square of an n n matrix? Just use a divide-and-conquer approach as in Strassen’s algorithm except that instead of getting 7 subproblems of
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