Article citationsMore>>

Yamazaki, I., Bai, Z., Simon, H., Wang, L. and Wu, K. (2010) Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method. ACM Transactions on Mathematical Software, 37, Article No. 27.
https://doi.org/10.1145/1824801.1824805

has been cited by the following article:

• TITLE: A New Type of Restarted Krylov Methods

  AUTHORS: Achiya Dax

  KEYWORDS: Restarted Krylov Methods, Exterior Eigenvalues, Symmetric Matrices, Monotonicity, Starting Vectors

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.7 No.1, March 31, 2017

  ABSTRACT: In this paper we present 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 polynomial filtering. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the eigenvalues toward their limits. The Krylov matrices that we use lead to fast rate of convergence. Numerical experiments illustrate the usefulness of the proposed approach.