What Is Strassen Matrix Multiplication Algorithm
Dynamic Programming Set 8 Matrix Chain Multiplication - GeeksforGeeks. Strassens had given another algorithm for finding the matrix multiplication.
Performance Of Strassen Matrix Multiplication Algorithm On Linux Ubuntu 16 04 Lts Vtr 064
Divide and Conquer Method Consider two matrices A and B with 4x4 dimension each as shown below The matrix multiplication of the above two matrices A and B is Matrix C.
What is strassen matrix multiplication algorithm. For a 2x2 matrix Strassens algorithm morphs an algorithm that needs 8 multiplications to one that needs 7 multiplications and leverages the distributive property to merge two multiplications into one operation and instead takes away from the new fatter node to extract one product term or the other etc. This preview shows page 19 - 22 out of 31 pages. The Algorithm multiplied by the Strassen matrix is compared to a normal algorithm but only one multiplication there are many time complexity.
The number of scalar additions and subtractions used in Strassens matrix multiplication algorithm is ________. In this algorithm the input matrices are divided into n2 x n2 sub matrices and then the recurrence relation is applied. Partition b into four sub matrices b11 b12 b21 b22.
Strassens Matrix multiplication can be performed only on square matrices where n is a power of 2. A Show that the exact solution is T N a 3 1 N log 2 7 2-a 3 N. Else Partition a into four sub matrices a11 a12 a21 a22.
It can be seen that a small difference may lead to a. Before jumping to Strassens algorithm it is necessary that you should be familiar with matrix multiplication using the Divide and Conquer method. Idea - Block Matrix MultiplicationThe idea behind Strassens algorithm is in the formulationof matrix multiplication as a recursive problem.
Divide X Y and Z into four n2 n2 matrices as represented below. In this context using Strassens Matrix multiplication algorithm the time consumption can be improved a little bit. Order of both of the matrices are n n.
This needs k2 multiplications and you get a kk matrix out at the end. Algorithm for Strassens matrix multiplication. Strassens Matrix Multiplication algorithm is the first algorithm to prove that matrix multiplication can be done at a time faster than ON3.
The Strassens method of matrix multiplication is a typical divide and conquer algorithm. Strassens is used to multiply two matrices but Matrix Chain Multiplication is an algorithm which doesnt multiply matrices. Strassens Matrix Multiplication Algorithm The major work in matrix multiplication is multiplication only.
So the idea is- if we reduced the number of multiplications then that will make the matrix multiplication faster. B Find an approximation to N 0 such that T N 0 T DEF N 0 when a 15. Think instead of multiplying a k1 vector by a 1k vector.
Strassens Matrix Multiplication Algorithm. We rst cover a variant of the naive algorithmformulated in terms of block matrices and then parallelize it. It utilizes the strategy of divide and conquer to reduce the number of recursive multiplication calls from 8 to 7 and hence the improvement.
Strassens matrix multiplication algorithm follows divide and conquer technique. Matrices Strassens multiplication algorithm leads to a recurrence of the form T N 7 T N 4 aN 4 N 1 T 1 1 N 1 where N n 2 is the number of entries of the matrices. B2RnnandCABwherenis a power of two2We writeAandBas block matrices.
When the size of the matrices to be multiplied is 2 x 2 Strassens algorithm carries out 7 multiplications and 24 additions whereas the regular multiplication requires 8 multiplications and 4 additions. It just gives the sequence in which a chain of matrices to be multiplied so that number of multiplications between matrix elements are minimum. However lets get again on whats behind the divide and conquer approach and implement it.
We have discussed Strassens Algorithm here. So I can do something like this by the definition of the Θ notation 31 c 1 2 l. The only thing thats different here is that the elements of your vector are nn matrices so youll wind up doing O k2 n log 7 scalar multiplications if you use Strassens algorithm to multiply nn matrices.
Strassens method is similar to above simple divide and conquer method in the sense that this method also divide matrices to sub-matrices of size N2 x N2 as shown in the above diagram but in Strassens method the four sub-matrices of result are calculated using following formulae. Algorithm Strassenn a b d begin If n threshold then compute C a b is a conventional matrix.
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