NVIDIA Corporation
Hierarchical Jacobi methods and systems implementing a dense symmetric eigenvalue solver

Abstract:

Embodiments of the present invention provide a hierarchical, multi-layer Jacobi method for implementing a dense symmetric eigenvalue solver using multiple processors. Each layer of the hierarchical method is configured to process problems of different sizes, and the division between the layers is defined according to the configuration of the underlying computer system, such as memory capacity and processing power, as well as the communication overhead between device and host. In general, the higher-level Jacobi kernel methods call the lower level Jacobi kernel methods, and the results are passed up the hierarchy. This process is iteratively performed until a convergence condition is reached. Embodiments of the hierarchical Jacobi method disclosed herein offers controllability of Schur decomposition, robust tolerance for passing data throughout the hierarchy, and significant cost reduction on row update compared to existing methods.