What is Strassen matrix multiplication algorithm?

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 does Strassen algorithm work?

Strassen’s Algorithm is an algorithm for matrix 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.

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)

Why is Strassen matrix multiplication better?

Strassen’s algorithm for matrix multiplication just gives a marginal improvement over the conventional O(N^3) algorithm. It has higher constant factors and is much harder to implement.

What is the complexity of Strassen’s algorithm?

As I mentioned above the Strassen’s algorithm is slightly faster than the general matrix multiplication algorithm. The general algorithm’s time complexity is O(n^3), while the Strassen’s algorithm is O(n^2.80).

What is the runtime of Strassen’s algorithm?

Strassen’s Algorithm makes only seven recursive calls, so it runs in time O(nlog2 7) = O(n2. 807…), faster than O(n3).

What type of algorithm is Strassen’s algorithm?

1. Strassen’s algorithm is a/an_____________ algorithm. Explanation: Strassen’s Algorithm for matrix multiplication is a recursive algorithm since the present output depends on previous outputs and inputs.

Why are matrix operations faster?

Generally, this way of multiplying two n-by-n matrices together requires n3 multiplications along the way. As matrices grow larger, the number of multiplications needed to find their product increases much faster than the number of additions.

What is the average time complexity of merge sort algorithm?

Time complexity of Merge Sort is O(n*Log n) in all the 3 cases (worst, average and best) as merge sort always divides the array in two halves and takes linear time to merge two halves. It requires equal amount of additional space as the unsorted array.

Can you multiply a 2×3 and 2×2 matrix?

Two matrices can only be multiplied when the number of columns of the first matrix is equal to the number of rows of the second matrix. For example, multiplication of 2×2 and 2×3 matrices is possible and the result matrix is a 2×3 matrix.

How to use Strassen’s algorithm for matrix multiplication?

I am having a hard time doing 4×4 matrix multiplication using strassen’s algorithm. First I computed the product of two 4×4 matrices using default matrix multiplication ( https://matrixcalc.org)

How did Strassen prove the runtime was not optiomal?

It was the first algorithm to prove that the basic O (n^3) runtime was not optiomal. The basic idea behind Strassen’s algorithm is to split A & B into 8 submatricies and then recursively compute the submatricies of C. This strategy is called Divide and Conquer.

When did Volker Strassen publish his first algorithm?

Volker Strassen first published his algorithm in 1969. It was the first algorithm to prove that the basic O (n^3) runtime was not optiomal. The basic idea behind Strassen’s algorithm is to split A & B into 8 submatricies and then recursively compute the submatricies of C. This strategy is called Divide and Conquer.

Which is better Strassen’s method or naive method?

Generally Strassen’s Method is not preferred for practical applications for following reasons. The constants used in Strassen’s method are high and for a typical application Naive method works better. For Sparse matrices, there are better methods especially designed for them.