An improved mixed-precision FEAST algorithm for solving symmetric eigenvalue problems

Solving symmetric eigenvalue problems is vital in many areas of scientific computing. FEAST is a well-known package designed for large-scale eigenvalue problems, incorporating mixed-precision techniques to accelerate linear equation solving. Unlike FEAST’s approach, this work introduces a new mixed-precision method that approximates the original eigenvalue problem at a lower precision to quickly provide a good initial guess. These results are then used to accelerate the convergence in working precision. Extensive experiments on large sparse matrices from real applications and randomly generated banded matrices demonstrate the effectiveness of this approach. In appropriate circumstances, our improved mixed-precision FEAST algorithm achieves an average speedup of 1.58× compared to the double-precision FEAST algorithm, with a maximum speedup of 1.79×. Additionally, compared to the original mixed-precision approach in the latest FEAST library, our method offers up to a 1.43× performance improvement.