  EigenDecomposition (ED) is at the heart of many computer vision algorithms
and applications. One crucial bottleneck limiting its usage is the expensive
computation cost, particularly for a mini-batch of matrices in the deep neural
networks. In this paper, we propose a QR-based ED method dedicated to the
application scenarios of computer vision. Our proposed method performs the ED
entirely by batched matrix/vector multiplication, which processes all the
matrices simultaneously and thus fully utilizes the power of GPUs. Our
technique is based on the explicit QR iterations by Givens rotation with double
Wilkinson shifts. With several acceleration techniques, the time complexity of
QR iterations is reduced from $O{(}n^5{)}$ to $O{(}n^3{)}$. The numerical test
shows that for small and medium batched matrices (\emph{e.g.,} $dim{<}32$) our
method can be much faster than the Pytorch SVD function. Experimental results
on visual recognition and image generation demonstrate that our methods also
achieve competitive performances.
