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Mixed-Precision Algorithm for Finding Selected Eigenvalues and Eigenvectors of Symmetric and Hermitian Matrices
SessionWorkshop on Latest Advances in Scalable Algorithms for Large-Scale Heterogeneous Systems (ScalAH'22)
DescriptionThe multi-precision methods commonly follow approximate-iterate scheme by first obtaining the approximate solution from a low-precision factorization and solve. Then, they iteratively refine the solution to the desired accuracy that is often as high as what is possible with traditional approaches. While targeting symmetric/Hermitian eigenvalue problems of the form Ax=(lambda)x, we revisited the SICE algorithm by applying the Sherman-Morrison formula on the diagonally-shifted tridiagonal systems, we propose an updated SICE-SM algorithm. We exploited asynchronous scheduling techniques to take advantage of the new computational graph enabled by the use of mixed-precision in the eigensolver. By incorporating the latest two-stage algorithms from the PLASMA and MAGMA software libraries for numerical linear algebra, we achieved up to 3.6x speedup using the mixed-precision eigensolver with the blocked SICE-SM algorithm for iterative refinement when compared with full double complex precision solvers for the cases with a portion of eigenvalues and eigenvectors requested.
Extreme Scale Computing
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