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Freitag, M.A. and Spence, A. (2009) The Calculation of the Distance to Instability by the Computation of a Jordan Block, Linear and Nonlinear Eigen Problems for PDEs, 274-275.

has been cited by the following article:

• TITLE: A Block-Preconditioned Inexact Linear Solver for Computing the Complex Eigenpairs of a Large Sparse Matrix

  AUTHORS: Richard Olatokunbo Akinola, Stephen Yakubu Kutchin, Ayodeji Sunday Ayodele, Kingsley Obiajulu Muka

  KEYWORDS: Preconditioner, Superlinear Convergence, Quadratic Convergence, Eigenvalues

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.2, February 28, 2018

  ABSTRACT: In computing eigenpairs of the matrix pencil, one obtains a linear system of equations. In this work, we show how a block triadiagonal preconditioner in GMRES can be used to solve a large sparse unsymmetric system of equations inexactly using a fixed and decreasing tolerance. While the fixed tolerance solver converged superlinearly to the eigenvalue of interest, the decreasing one converged quadratically. This surpasses an earlier result which converged harmonically.