Can we solve matrix multiplication using recursion?

First check if multiplication between matrices is possible or not. For this, check if number of columns of first matrix is equal to number of rows of second matrix or not. In Recursive Matrix Multiplication, we implement three loops of Iteration through recursive calls.

What is the time complexity of matrix multiplication algorithm when divide and conquer strategy is applied?

Time Complexity of above method is O(N3). Following is simple Divide and Conquer method to multiply two square matrices. 1) Divide matrices A and B in 4 sub-matrices of size N/2 x N/2 as shown in the below diagram.

What do you mean by 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.

Which data structure is used in recursion?

stacks
Many programming languages implement recursion by means of stacks. Generally, whenever a function (caller) calls another function (callee) or itself as callee, the caller function transfers execution control to the callee.

How many multiplications are required for Strassen’s matrix multiplication?

In Strassen’s matrix multiplication there are seven multiplication and four addition, subtraction in total.

How do you find the complexity of a matrix multiplication?

The standard way of multiplying an m-by-n matrix by an n-by-p matrix has complexity O(mnp). If all of those are “n” to you, it’s O(n^3), not O(n^2).

How do you solve a matrix multiplication problem using divide and conquer?

Strassen’s algorithm has four steps:

1. Divide the input matrices A and B into n/2 x n/2 submatrices, which takes Θ(1) time by performing index calculations.
2. Create 10 matrices S1 , S2 , S3 , …
3. Using the submatrices created from both of the steps above, recursively compute seven matrix products P1 , P2 , … P7 .