Limitation of strassen algorithm for matrix multiplication
Answers
Answer:
Limitations:-
Explanation:
1) Strassen's algo is not quite as numerically stable as the naive method.
2) Sub-matrices formed at the levels of recursion consume space.
3) When matrices are sparse, methods tailored for sparse matrices are faster.
4) It would be slower for extremely large matrices.
5) Constant factors hidden in the running time of this algo is larger.
Answer:- The limitations of the Strassen algorithm for matrix multiplication are :-
1. Strassen's algorithm is not like the numerically stable algorithms as the other naive method.
2. The Sub-matrices formed at the levels of recursion consume much space.
3. When the matrices are sparse, then the methods tailored for sparse matrices are faster.
4. This method would be slower for the extremely large matrices provided to work on.
5. The Constant factors are hidden in the running time of this algorithm is too large.
The Strassen’s method of matrix multiplication is the typical divide and conquer algorithm. The matrix multiplication is one of the most fundamental operations in the Machine learning and optimizing. It is a key to the several optimizations. In general, multiplying the two matrices of size N X N takes the N^3 operations.
Usually, the Strassen’s Method is not preferred for the practical applications for following reasons:-
1. The constants that are used in Strassen’s method are high and are for a typical application Naive method works better.
2. For the Sparse matrices, there are better methods especially designed for them to use.
3. The submatrices in recursion take extra space in it.
4. Because of the limited precision of the computer arithmetic on the Non integer values, the larger errors accumulate in the Strassen’s algorithm than in Naive Method.
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