We present a parallel divide-and-conquer matrix multiplication algorithm whose natural communication structures is the hypercube. The complexity of the algorithm is O(log n) using n3/2 processors and O(n) using O(n2) processors. We show how to use the algorithm for practical computing giving ...
Using these equations to define a divide and conquer strategy we can get the relation among them as: T(N) = 8T(N/2) + O(N2)From the above we see that simple matrix multiplication takes eight recursion calls.T(n)=O(n^3)Thus, this method is faster than the ordinary one.It takes ...
Divide and Conquer Once we have completed the preliminary explanations, we can shift our attention to the core of this article. The Order of Matrix Multiplication Now that we understand matrix multiplication, we can discuss its order. One of the key—yet often overlooked—aspects of transformations...
First of all, matrix multiplication can be thought of as a sequence of vector–matrix multiplications: (8.8)An×m⋅Bm×l:=(a1T⋅Ba2T⋅B⋮anT⋅B), where aiT is the ith row of A, and aiT ⋅ B is a vector–matrix multiplication. Note that fB(aiT):=aiT ⋅ B is a linea...
You might be able to write a 'divide and conquer' algorithm to implement the matrix multiplication using the GPU to perform the actual multiplications, however whether this beats the multi-threaded CPU implementation in MATLAB would depend a lot not only on the GPU you have, but also the ...
m[i][j] = t; //record the smallest multiplication s[i][j] = k; //record the location of split } } } } traceBack(1, 5, s); } int main(void) { int s[] = {3, 2, 5, 10, 2, 3}; matrixChain(s, 6); return 0; ...
a recursive ‘divide-and-conquer’ structure for generalized matrix multiplication. This algorithm is an adaptation of an earlier demonstration algorithm for square matrices [3], which resembles the standard recursive block algorithm for MM. We implemented the Cilk algorithm under Linux sys- ...
Consider any known sequential algorithm for matrix multiplication over an arbitrary ring with time complexity O(Nα), where 2 < α<3. We show that such an algorithm can be parallelized on a distributed memory parallel computer (DMPC) in O (log N) time by using...
We propose a divide-and-conquer strategy to discover hierarchical community structure, nonoverlapping within each level. Our algorithm is based on the highly efficient rank-2 symmetric nonnegative matrix factorization. We solve several implementation challenges to boost its efficiency on modern computer ar...
The set of orthogonal matrices V ∈ ℝn×n is closed under multiplication and constitutes the orthogonal group O(n). Indeed, given two orthogonal matrices V and U, we find that (2.34)VUVUT=VUUTVT=I. Since det(VTV) = (detV)2 = 1, we have detV = ±1. The set of orthogonal ma...