Howtosignalprocessing
- What is the complexity of matrix multiplication?
- What is the space complexity of matrix chain multiplication?
- Which of the models has a complexity of n for matrix multiplication?
- What is the time complexity of sparse matrix multiplication?
What is the complexity of matrix multiplication?
As of October 2022, the best announced bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.37188) time, given by Duan, Wu and Zhou announced in a preprint. This improves on the bound of O(n2.3728596) time, given by Josh Alman and Virginia Vassilevska Williams.
What is the space complexity of matrix chain multiplication?
Complexity Analysis
Hence, the overall time complexity is O ( n 3 ) O(n^3) O(n3). Space Complexity - We are using an auxiliary d p dp dp array of dimensions, ( n − 1 ) × ( n − 1 ) (n-1)\times(n-1) (n−1)×(n−1) hence space complexity is O ( n 2 ) O(n^2) O(n2)
Which of the models has a complexity of n for matrix multiplication?
The fastest known matrix multiplication algorithm is Coppersmith-Winograd algorithm with a complexity of O(n2.3737). Unless the matrix is huge, these algorithms do not result in a vast difference in computation time.
What is the time complexity of sparse matrix multiplication?
The computational complexity of sparse matrix multiplication on AP is shown to be an O(nnz) where nnz is the number of nonzero elements. The AP is found to be especially efficient in binary sparse matrix multiplication.
