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.