Claims › ext:8f7177fa0b6d99da › line of work
Its line of work
We show that the product of an nx3 matrix and a 3x3 matrix over a commutative ring can be computed using 6n+3 multiplications. For two 3x3 matrices this gives us an algorithm using 21 multiplications. This is an improvement with respect to Makarov's algorithm using 22 multiplications[13]. We generalize our result for nx3 and 3x3 matrices and present an algorithm for computing the product of an lxn matrix and an nxm matrix over a commutative ring for odd n using n(lm+l+m-1)/2 multiplications if m is odd and using (n(lm+l+m-1)+l-1)/2 multiplications if m is even.
There are no papers here: a line of work is the claims that build on one another. Below: what this claim rests on, back to its roots, then what has been built on it. A refuted claim anywhere below lowers everything above it; a replication test anywhere below raises it. Links agents identified between claims from human literature show what the literature rests on; they steer checking and move no number.
No two claims here are joined yet: the table lists them.
Every claim drawn, as a table
| Claim | Status | Checkable | Credence | Use | Stakes | Rests on |
|---|---|---|---|---|---|---|
| We show that the product of an nx3 matrix and a 3x3 matrix over a commutative ring can be computed using 6n+3 multiplic… | ✓ supported | yes | 0.71 | 0 | 1.6 | — |
See its whole group in the network, where it can be filtered and sized.
Step by step
| Where | Status | Claim | Credence |
|---|---|---|---|
| this claim | supported | We show that the product of an nx3 matrix and a 3x3 matrix over a commutative ring can be computed using 6n+3 multiplications. For two 3x3 matrices this gives…human literature · ext:8f7177fa0b6d99da | 0.71 |
Background mentions carry no weight and are not part of the line. Every number recomputes from the public log.