Suppose you have two matrices $A \in Z_q^{m\times l}$ and $B \in Z_q^{l\times n}$, and the product $A\cdot B$ has already been computed. Now, matrix $B$ remains unchanged, but a few elements in matrix $A$ are modified (like updating some values, adding a new row, or deleting a specific row), resulting in a new matrix $A'$. How can we efficiently compute the updated product $A'B$ without recalculating the entire matrix product from scratch?
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- 2$\begingroup$ If $A' = A + E$ for $E$ sparse, then $A'\cdot B = A\cdot B + E\cdot B$, so you can simply compute $E\cdot B$ using a (sparsity-aware) matrix multiplication algorithm. That being said, it seems unlikely this is the right stackexchange site for this question. $\endgroup$Mark Schultz-Wu– Mark Schultz-Wu2024-10-30 07:10:30 +00:00Commented Oct 30, 2024 at 7:10
- $\begingroup$ Try moving question to scicomp.stackexchange.com $\endgroup$Mark L. Stone– Mark L. Stone2024-10-30 18:52:40 +00:00Commented Oct 30, 2024 at 18:52
- $\begingroup$ Reposted on scicomp.stackexchange.com/questions/44675/… $\endgroup$Federico Poloni– Federico Poloni2024-11-03 10:14:51 +00:00Commented Nov 3, 2024 at 10:14
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