We use cookies to ensure you have the best browsing experience on our website. Don’t stop learning now. This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Strassen’s Algorithm”.1. You can find a tip somewhere at the end of the article on how to generalize this algorithm for any value of n.For multiplying two matrices of size n x n, we make 8 recursive calls above, each on a matrix/subproblem with size n/2 x n/2. Active 1 year, 4 months ago. Who discussed techniques for reducing the memory requirements for Strassen’s algorithm?11. Compute the product matrix using Strassen’s matrix multiplication algorithm.To practice all areas of Data Structures & Algorithms,
Divide and Conquer Method. Divide and Conquer | Set 5 (Strassen’s Matrix Multiplication) Easy way to remember Strassen’s Matrix Equation; Largest Square in a Binary Matrix with at most K 1s for multiple Queries; Median of an unsorted array using Quick Select Algorithm; Check if a string is a scrambled form of another string; Count of smaller elements on right side of each element in an Array using Merge sort ; … Strassen’s algorithm is quite numerically stable as the naïve method.15. In this article, we are going to discuss about the strassen matrix multiplication, formula of matrix multiplication and algorithms for strassen matrix multiplication. Get hold of all the important DSA concepts with the Who demonstrated the difference in numerical stability?9. so, a > b k as 7 > 2 2.
In Recursive Matrix Multiplication, we implement three loops of Iteration through recursive calls. Hello I am trying to get the efficiency for Strassen's algorithm but need some help. By using our site, you Before jumping to Strassen's algorithm, it is necessary that you should be familiar with matrix multiplication using the Divide and Conquer method. How many iterating statements are involved in the naïve method of matrix multiplication?14.
What is the running time of naïve matrix multiplication algorithm?4. By using our site, you acknowledge that you have read and understand our Featured on Meta What is the running time of Strassen’s algorithm for matrix multiplication?3. Efficiency class ? Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.
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Stack Overflow works best with JavaScript enabled This is recurrence equation for Strassen`s method of matrix multiplication. Addition of two matrices takes O(NGenerally Strassen’s Method is not preferred for practical applications for following reasons.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed aboveAttention reader! What is the formula to calculate the element present in second row, first column of the product matrix?12. All Rights Reserved. Order of both of the matrices are n × n. acknowledge that you have read and understood our Before jumping to Strassen's algorithm, it is necessary that you should be familiar with matrix multiplication using the 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,Now, let's look at the Divide and Conquer approach to multiply two matrices.Take two submatrices from the above two matrices A and B each as ($A_{11}$ & $A_{12}$) and ($B_{11}$ & $B_{21}$) as shown below,And the matrix multiplication of the two 2x2 matrices A11 and B11 is,Also, the matrix multiplication of two 2x2 matrices A12 and B21 is as follows,$A_{11}*B_{11} + A_{12}*B_{21} = \begin{bmatrix}And $c_{11}$, $c_{12}$, $c_{21}$ and $c_{22}$ are equal to equations 1, 2, 3 and 4 respectively.So the idea is to recursively divide n x n matrices into n/2 x n/2 matrices until they are small enough to be multiplied in the naive way, more specifically into 8 multiplications and 4 matrix additions as shown below in the code.Note: Here the dimension n is of the power of 2. This being Strassen the point was to show that the complexity is better than $\Theta(n^3),$ the naive matrix multiplication, which it is, because $\log_2 7 < 3$.