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Results tagged with multiplication
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user 535
3
votes
Why is the transform in Schönhage–Strassen's multiplication algorithm cheap?
There's an excellent explanation of exactly what's going on, including how the size of the field goes down as you progress, in GMP's documentation: 15.1.6 FFT Multiplication. …
- 5,902
3
votes
Where does the lg(lg(N)) factor come from in Schönhage–Strassen's run time?
The issue is that the expansion factor inside the recursive term is not less than 2, and that causes the bound to fail. Define:
$T_c(n) = n \log n + \sqrt n T(c \sqrt n)$
I claim that $T_{2-\epsilon …
- 5,902
2
votes
Does the performance of matrix multiplication depend on the storage of the array?
It depends on the machine model you're using.
In the RAM model, which is probably the most commonly used one, the complexity is the same regardless of the layout being row-major or column-major.
In …
- 5,902
6
votes
Accepted
Is matrix "adjoint-squaring" faster than general matrix multiplication?
You can reduce general matrix multiplication down to three "adjoint-squarings".
Suppose we're given an adjoint-squaring function $\mathfrak{F}$ where $\mathfrak{F}(M) = M \cdot M^\dagger$. … adjoint-squaring (it's certainly not the adding, conjugating, transposing, subtracting, or scaling), and the adjoint-squaring function $\mathfrak{F}$ is only used a constant number of times (3 times), general multiplication …
- 5,902