Matrix Multiplication By Strassen's Method

08 Apr, 2021

Strassens Matrix Multiplication Now that we have seen that the divide-and-conquer approach can reduce the number of one-digit multiplications in multiplying two integers we should not be surprised that a similar feat can be accomplished for multiplying matrices. Strassen 1969 showed that 2x2 matrix multiplication can be accomplished in 7 multiplications and 18 additions or subtractions 7 2Θ 2 Case 1 of Master Method2 2 7solution Θ.

Recursive Matrix Multiplication Strassen Algorithm Mathematics Stack Exchange

It reduces the 8 recursive calls to 7.

Matrix multiplication by strassen's method. C code of two 2 by 2 matrix multiplication using Strassen algorithm. Generally Strassens Method is not preferred for. Int a 2 2b 2 2c 2 2ij.

Int main. This method is introduced to reduce the complexity. The advantage of this algorithm is that it uses less number of operations then the naive method.

Given these shortcomings is strassens algorithm actually useful and is it. Such an algorithm was published by V. If A a b c d the multiplications are a a d d b a d c a d b c.

Idea - Block Matrix MultiplicationThe idea behind Strassens algorithm is in the formulationof matrix multiplication as a recursive problem. Strassen algorithm is a recursive method for matrix multiplication where we divide the matrix into 4 sub-matrices of dimensions n2 x n2 in each recursive step. Ae bg af bh ce dg and cf dh.

Strassens AlgorithmThe Strassens method of matrix multiplication is a typical divide and conquer algorithm. 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. We have seen so far some divide and conquer method as merge sort karatsubas fast multiplication of large numbers.

However lets get again on whats behind the divide and conquer approach and implement it. Order of both of the matrices are n n. Strassens Matrix Multiplication algorithm Pseudocode.

Fori0i. 2 Calculate following values recursively. B2RnnandCABwherenis a power of two2We writeAandBas block matrices.

We have discussed Strassens Algorithm here. We rst cover a variant of the naive algorithmformulated in terms of block matrices and then parallelize it. 1 Divide matrices A and B in 4 sub-matrices of size N2 x N2 as shown in the below diagram.

In the above method we do 8 multiplications for matrices of size N2 x N2 and 4 additions. Strassens algorithm for matrix multiplication just gives a marginal improvement over the conventional O N3 algorithm. It has higher constant factors and is much harder to implement.

Before jumping to Strassens algorithm it is necessary that you should be familiar with matrix multiplication using the Divide and Conquer method. Following is simple Divide and Conquer method to multiply two square matrices. 9 rows In linear algebra the Strassen algorithm named after Volker Strassen is an algorithm for.

Use the previous set of formulas to carry out 22 matrix multiplication. Design and Analysis of AlgorithmsStrassen matrixmultiplication divideandconquer. Printf Enter the 4 elements of first matrix.

Divide a matrix of order of 22 recursively till we get the matrix of 22. Using the same approach as of Strassens only 5 multiplications are sufficient to compute square of a matrix. It uses divide and conquer strategy and thus divides the square matrix of size n to n2.

The Strassens method of matrix multiplication is a typical divide and conquer algorithm. Divide X Y and Z into four n2 n2 matrices as represented below Z I J K L X A B C D and Y E F G H. In this method we use the algorithm given by Strassen.

Divide matrices A and B in 4 sub-matrices of size N2 x N2 as shown in the above diagram. Strassen in 1969 Str69. If we generalise this algorithm for getting the square of a matrix the complexity reduces to nlog5 with base 2.

Procedure of Strassen matrix multiplication There are some procedures. Strassens Matrix multiplication can be performed only on square matrices where n is a power of 2.

Recursive Matrix Multiplication Strassen Algorithm Mathematics Stack Exchange

Divide And Conquer Set 5 Strassen S Matrix Multiplication Tutorialspoint Dev

Pdf Comparative Study Of Strassen S Matrix Multiplication Algorithm

Recursive Matrix Multiplication Strassen Algorithm Mathematics Stack Exchange

Strassen S Matrix Multiplication Hindi Daa Example 1 Youtube

Write Strassen S Algorithm What Are The Limitation Of Strassen S Algorithim Apply Strassen S Algorithm To Multiply Two Matrices A1 A2 Given Below Ignou Free Assignments