The Use of Restarted Krylov Methods for Large Sparse Least Squares Problems
Abstract
ABSTRACT The use of restarted Krylov methods for solving large sparse linear least squares problems suffers from certain inherited difficulties. One of them arises in ill‐conditioned problems, when part of the residual vector is spanned by singular vectors that correspond to small singular values. The modification proposed in this article enables the Krylov subspaces to collect information on these vectors. This is achieved by combining the restarted Krylov process with the Heart iteration for computing small singular values. Numerical experiments illustrate the usefulness of the proposed approach.
Fields of Study & Subjects
Matrix Theory and Algorithms
Statistical and numerical algorithms
Neural Networks and Applications
Publication details
- Journal / source
- Numerical Linear Algebra with Applications
- Volume
- 33
- Issue
- 4
- Publication date
- 1 August 2026
- Language
- EN