1 citations · 1 across the 10 of their papers we have counts for
11 papers
A Modified Direct Eigenvalue Swapping Algorithm with Guaranteed Stability
Meiyue Shao, Rentao Xu
For a given matrix \( A \) in the real Schur form, the eigenvalue swapping algorithm is used to swap two adjacent diagonal blocks. In LAPACK, this operation is performed by the sub…
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…
On a shrink-and-expand technique for symmetric block eigensolvers
Yuqi Liu, Yuxin Ma, Meiyue Shao
In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block…
Mixed precision iterative refinement for least squares with linear equality constraints and generalized least squares problems
Bowen Gao, Yuxin Ma, Meiyue Shao
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem…
Improving performance of contour integral-based nonlinear eigensolvers with infinite GMRES
Yuqi Liu, Jose E. Roman, Meiyue Shao
In this work, the infinite GMRES algorithm, recently proposed by Correnty et al., is employed in contour integral-based nonlinear eigensolvers, avoiding the computation of costly f…
A Contour Integral-Based Algorithm for Computing Generalized Singular Values
Yuqi Liu, Xinyu Shan, Meiyue Shao
We propose a contour integral-based algorithm for computing a few singular values of a matrix or a few generalized singular values of a matrix pair. Mathematically, the generalized…