The Shifted-inverse Power Weak Galerkin Method for Eigenvalue Problems
Provides a more efficient numerical method for computing eigenvalue lower bounds, relevant to computational mathematics and engineering applications.
The paper introduces a shifted-inverse power weak Galerkin method for eigenvalue problems, achieving high-order lower bounds at low cost. Numerical examples validate the theoretical error estimates and asymptotic lower bounds.
This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a relatively low cost via the proposed method. The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions. Numerical examples are presented to validate the theoretical analysis.