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Efficiently compute parallel matrix-vector product for block vectors with FFTs?
Let's look at the case where $P=2$, for starters. The FFT can be computed in a divide-and-conquer fashion, where first we compute the FFT of the even-numbered indices, then the FFT of the odd-numbere …
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Could an NP-Hard problem be in P in after a basis transform?
Could a problem we think is NP-hard actually be solvable in polytime? Sure. We could be wrong (we suspected/guessed it was NP-hard, but our suspicion/guess was wrong). Or, it could be NP-hard and s …
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Morgenstern proof for FFT lower bound
Morganstern's original paper is here:
Jacques Morgenstern. Note on a lower bound on the linear complexity of the fast Fourier transform. J. ACM, 20(2):305–306, April 1973.