A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems
This work addresses the need for scalable eigenvalue computation in large Hermitian matrices, offering a practical tool for scientific computing applications.
The paper presents a Thick-Restart Lanczos algorithm with polynomial filtering for computing eigenvalues in a specified interval of a Hermitian matrix. The method enables efficient spectrum-slicing for large-scale eigenvalue problems.
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a Thick-Restart version of the Lanczos algorithm with deflation (`locking') and a new type of polynomial filters obtained from a least-squares technique. The resulting algorithm can be utilized in a `spectrum-slicing' approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different sub-intervals independently from one another.