Dax, A. (2019) Computing the Smallest Singular Triplets of a Large Matrix. Results in Applied Mathematic, 3, Article ID: 100006.
https://doi.org/10.1016/j.rinam.2019.100006

has been cited by the following article:

• 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.