# Paper Corrections for Butterfly Factorization

April 22, 2017

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.

• 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 …”

• 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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