Robust level-3 BLAS Inverse Iteration from the Hessenberg Matrix

Inverse iteration is known to be an effective method for computing eigenvectors corresponding simple and well-separated eigenvalues. In the non-symmetric case, solution of shifted Hessenberg systems a central step. Existing inverse solvers approach with either RQ or LU factorizations and, once factored, solve systems. This has limited level-3 BLAS potential since distinct shifts have factorizations. paper rearranges such that data shared between can exploited. Thereby backward substitution triangular R factor expressed mostly matrix–matrix multiplications (level-3 BLAS). The resulting algorithm computes in tiled, overflow-free, task-parallel fashion. numerical experiments show new outperforms existing computation both real complex eigenvectors.