TITLE:
A Compact Heart Iteration for Large Eigenvalues Problems
AUTHORS:
Achiya Dax
KEYWORDS:
Large Sparse Matrices, Restarted Krylov Methods, Exterior Eigenvalues, Symmetric Matrices, Monotonicity, Starting Vectors
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.12 No.1,
March
14,
2022
ABSTRACT: In this paper, we present a compact version of the Heart iteration. One that requires less matrix-vector products per iteration and attains faster convergence. The Heart iteration is a new type of Restarted Krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process and the use of implicit restarts. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the computed Ritz values toward their limits. Numerical experiments illustrate the usefulness of the proposed approach.