Paper Corrections for Butterfly Factorization
This post lists corrections for the following paper.
- Y. Li, H. Yang, E. Martin, K. Ho and L. Ying, Butterfly Factorization, Multiscale Modeling and Simulation 13:2, 714-732 (2015). [PDF, journal]
So far, I have found the following mistakes or typos.
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Page 719, Section 2.2, last sentence of the first paragraph “… hence requires only $O(r(m+n))$ operations and memory.” should be “… hence requires only $O(r^2(m+n))$ operations and $O(r(m+n))$ memory …”
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Page 718, Section 2.1, SVD via random matrix-vector multiplication. The formula for the middle matrix $ M = Q^\star_{col} Z Q_{row} $ in the third step should not be used in the middle level factorization directly, since the matrix Z could not be applied to basis $ Q_{row} $ or $ Q_{col} $ again. The actual way to implement is that $ M = \left( R^\star_{row}Q_{col} \right)^\dagger R^\star_{row} Z R_{col} \left( Q^\star_{row} R_{col} \right)^\dagger $. Such the case $ Z R_{col} $ can be reused and all the computations are in the local block.
Yingzhou Li
Discussion
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