Calculate eigenvalues/eigenvectors of hundreds of small matrices using CUDA

Question

I have a question on the eigen-decomposition of hundreds of small matrices using CUDA.

I need to calculate the eigenvalues and eigenvectors of hundreds (e.g. 500) of small (64-by-64) real symmetric matrices concurrently. I tried to implement it by the Jacobi method using chess tournament ordering (see this paper (PDF) for more information).

In this algorithm, 32 threads are defined in each block, while each block handles one small matrix, and the 32 threads work together to inflate 32 off-diagonal elements until convergence. However, I am not very satisfied with its performance.

I am wondering where there is any better algorithm for my question, i.e. the eigen-decomposition of many 64-by-64 real symmetric matrices. I guess the householder's method may be a better choice but not sure whether it can be efficiently implemented in CUDA. There are not a lot of useful information online, since most of other programmers are more interested in using CUDA/OpenCL to decompose one large matrix instead of a lot of small matrices.

Answer 1

At least for the Eigenvalues, a sample can be found in the Cuda SDK

http://www.nvidia.de/content/cudazone/cuda_sdk/Linear_Algebra.html

Images seem broken, but download of samples still works. I would suggest downloading the full SDK and having a look at that exsample. Also, this Paper could be helpfull:

http://docs.nvidia.com/cuda/samples/6_Advanced/eigenvalues/doc/eigenvalues.pdf