Implementations of main algorithms for generalized symmetric eigenproblem on GPU accelerator

Abstract

To solve a generalized eigensystem problem, we firstly need to transform the generalized eigenproblem to a standard eigenproblem, and then reduce a matrix to tridiagonal form. These are based on both blocked Cholesky decomposition and blocked Householder tridiagonalization method. We present parallel implementations of standard transformation which combines the Cholesky into the transformation from generalized to standard form, and reduction of a dense matrix to tridiagonal form on GPU accelerator using CUBLAS. Experimental results clearly demonstrate the potential of data-parallel coprocessors for scientific computations. When comparing against the CPU implementation, the GPU implementations achieve above 16-fold and 20-fold speedups in double precision respectively.