How do you solve Strassen matrix multiplication?

Strassen’s Matrix Multiplication Algorithm

  1. M1:=(A+C)×(E+F)
  2. M2:=(B+D)×(G+H)
  3. M3:=(A−D)×(E+H)
  4. M4:=A×(F−H)
  5. M5:=(C+D)×(E)
  6. M6:=(A+B)×(H)
  7. M7:=D×(G−E)

What is Strassen matrix problem?

Strassen in 1969 which gives an overview that how we can find the multiplication of two 2*2 dimension matrix by the brute-force algorithm. But by using divide and conquer technique the overall complexity for multiplication two matrices is reduced.

What is Strassen multiplication?

Strassen algorithm is a recursive method for matrix multiplication where we divide the matrix into 4 sub-matrices of dimensions n/2 x n/2 in each recursive step. For example, consider two 4 x 4 matrices A and B that we need to multiply. A 4 x 4 can be divided into four 2 x 2 matrices.

What is the complexity of Strassen matrix multiplication?

Strassen’s Submatrix The time complexity using the Master Theorem. T(n) = 7T(n/2) + O(n^2) = O(n^log(7)) runtime.

How do you learn the Strassen formula?

Come Back to P2 : we have H there and it’s adjacent element in X Matrix is D, since X is Row Matrix so we select a Row in X such that D won’t come, we find A B Column, so multiply H with (A + B)…Easy way to remember Strassen’s Matrix Equation

  1. AHED (Learn it as ‘Ahead’)
  2. Diagonal.
  3. Last CR.
  4. First CR.

Why is Strassen matrix multiplication better?

Strassen’s matrix multiplication (MM) has benefits with respect to any (highly tuned) implementations of MM because Strassen’s reduces the total number of operations. Strassen achieved this operation reduction by replacing computationally expensive MMs with matrix additions (MAs).

What is the purpose of Strassen matrix multiplication?

In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for large matrices, with a better asymptotic complexity, although the naive algorithm is often better for smaller matrices.

How do you memorize Strassen matrix?

Remember Counting : Write P1 + P2 at C2. Write P3 + P4 at its diagonal Position i.e. at C3. Write P4 + P5 + P6 at 1st position and subtract P2 i.e. C1 = P4 + P5 + P6 – P2. Write odd values at last Position with alternating – and + sign i.e. P1 P3 P5 P7 becomes C4 = P1 – P3 + P5 – P7.

Is Strassen matrix multiplication better than ordinary multiplication?

The results show that Strassen’s algorithm needs more memory allocations than the conventional algorithm, due to the fact in design that more arrays need to be created. I. Introduction The multiplication of two matrices is one of the most important operations in linear algebra.

Why is Strassen matrix multiplication considered better than simple matrix multiplication?

Why we use Strassen matrix multiplication?