7 papers
Field-of-values analysis of augmented Krylov methods for matrix -function actions
Xiaobo Liu, Marcel Schweitzer
We revisit established Krylov subspace methods for linear combinations of matrix -function actions from the viewpoint of the block triangular formulation of Al-Mohy and Liu [SI…
Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences
Pascal den Boef, Patrick Kürschner, Xiaobo Liu +5
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In thi…
Mixed-precision iterative refinement for low-rank Lyapunov equations
Peter Benner, Xiaobo Liu
We develop a mixed-precision iterative refinement framework for solving low-rank Lyapunov matrix equations , where or . Via rounding error analy…
A Novel Approach for Flexible Body Dynamics Computation via Synthesizing Incremental Motions in Reconfigured Inertial Frames
Xiaobo Liu
A novel approach is presented for computing flexible body dynamics based on conventional structural dynamics models. This approach innovatively captures the rigid body motion compo…
A scaling and recovering algorithm for the matrix -functions
Awad H. Al-Mohy, Xiaobo Liu
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix -functions that arise in exponential integrator methods for the numerical solution of…
A note on the cross matrices
Xiaobo Liu
A cross matrix can have nonzero elements located only on the main diagonal and the anti-diagonal, so that the sparsity pattern has the shape of a cross. It is shown that ca…