10 papers
A mixed precision algorithm for the matrix square root
Bowen Gao, Daniel Kressner, Meiyue Shao
Mixed precision algorithms can significantly enhance the performance of linear algebra solvers by leveraging increasingly powerful low precision hardware while recovering working p…
Linear convergence of iterative contour integral-based eigensolvers for nonlinear eigenvalue problems
Daniel Kressner, Yuqi Liu, Jose E. Roman +2
Solving nonlinear eigenvalue problems is an important and challenging task in scientific computing. Contour integral-based approaches are attractive for such eigenvalue problems be…
On Two-Stage Householder Orthogonalization
Zhuang-Ao He, Meiyue Shao
Two-stage orthogonalization is essential in numerical algorithms such as Krylov subspace methods. For this task we need to orthogonalize a matrix against another matrix wit…
Mixed precision thin SVD algorithms based on the Gram matrix
Erin Carson, Yuxin Ma, Meiyue Shao
In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices…
On Eigenvector Computation and Eigenvalue Reordering for the Non-Hermitian Quaternion Eigenvalue Problem
Zhigang Jia, Meiyue Shao, Yanjun Shao
In this paper we present several additions to the quaternion QR algorithm, including algorithms for eigenvector computation and eigenvalue reordering. A key outcome of the eigenval…
Solving nonlinear eigenvalue problems via contour integration and region partitioning
Yuqi Liu, Jose E. Roman, Meiyue Shao
In this work, we combine Beyn's method and the recently developed recursive integral method (RIM) to propose a contour integral-based, region partitioning eigensolver for nonlinear…