From the 1 of 10 linked papers with an AI index.
10 papers
A mixed precision algorithm for the matrix square root
Bowen Gao, Daniel Kressner, Meiyue Shao
The paper introduces a mixed‑precision method for computing matrix square roots that uses a low‑precision Schur decomposition followed by iterative refinement via an approximate Ne…
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…
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…
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…