Fault Tolerance through Invariant Checking for the Lanczos Eigensolver

The Lanczos eigensolver is a popular iterative method for approximating a few maximal eigenvalues of a real symmetric matrix, particularly if the matrix is large and sparse. In recent years, graphics processing units (GPUs) have become a popular platform for scientific computing applications, many of which are based on linear algebra, and are increasingly being used as the main computational units in supercomputers. This trend is expected to continue as the number of computations required by scientific applications reach petascale and exascale range. In this paper, we introduce an efficient error checking mechanism for the Lanczos eigensolver. To the best of our knowledge, we are the first to introduce such a scheme for the Lanczos method. We evaluate our fault tolerant scheme using an open-source sparse eigensolver on a GPU platform, with and without the injection of faults. We use sparse matrices from real applications, and show that our fault tolerant method has good error coverage and low overhead.