A Memory-Efficient Algorithm for Large-Scale Symmetric Tridiagonal Eigenvalue Problem on Multi-GPU Systems

Divide-and-conquer algorithm is a numerically stable and efficient algorithm that computes the eigenvalues and eigenvectors of a symmetric tridiagonal matrix. We often face the situation where the input matrix fits into the main memory but not into the on-chip memory of a GPU device. We present an out-of-core implementation where only part of the input matrix is resident in GPU memory at any point in time. It works independently of the physical size of GPU memory, handling any size of input as long as it fits into the main memory. Work is dynamically allocated to multiple GPUs and CPU cores, taking account of available workspaces and progress of the algorithm. In addition, it delivers a performance comparable to that of conventional multi-GPU implementations for cases where workspaces fit into the GPU memory.