Iterative refinement for an eigenpair subset of a real symmetric matrix

Numerical computation for eigenvalue decomposition plays a crucial role in many scientific fields, and highly accurate eigenpairs are required in certain domains. A novel method was proposed in this study for the iterative refinement of the eigenpair of a real symmetric matrix, which is based on the Ogita–Aishima method and uses compact WY representation. The proposed method can refine the accuracy of a partial eigenpair without using a full eigenvector matrix. Numerical examples illustrate the convergence of residuals, and a large-memory computer is not required for refinement.