Adaptive Polynomial Filtering for Hermitian Interior Eigenproblems: Convergence Analysis
This addresses computational bottlenecks in scientific computing for eigenvalue problems, though it appears incremental as an enhancement to existing filtered subspace methods.
The paper tackles interior eigenvalue problems for large-scale sparse Hermitian matrices by proposing an adaptive polynomial filtering strategy integrated into filtered subspace iteration, establishing convergence bounds and incorporating spurious eigenvalue detection. Numerical results demonstrate improved efficiency and robustness compared to classical approaches.
Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a filtered subspace iteration framework. We establish pointwise convergence bounds in both undamped and damped settings and incorporate an enhanced spurious eigenvalue detection technique to improve efficiency and robustness. At the implementation level, we employ MaSpMM to accelerate the polynomial filtering step. Numerical results demonstrate the efficiency and robustness of the proposed method compared with classical approaches.