The Convergence Rate of the Chebyshev SIM Under a Perturbation of a Complex Line-Segment Spectrum
Linear Algebra and Its Applications
The Chebyshev semiiterative method (chsim) is probably the best known and most often used method for the iterative solution of linear system x = Tx + c, where the spectrum of T is located in a complex line segment [α, β] excluding 1. The asymptotic convergence factor (ACF) of the chsim, under a perturbation of [α, β], is considered. Several formulae for the approximation to the ACFs, up to the second order of a perturbation, are derived. This generalizes the results about the sensitivity of the asymptotic rate of convergence to the estimated eigenvalues by Hageman and Young in the case that both α and β are real. Two numerical examples are given to illustrate the theoretical results.
"The Convergence Rate of the Chebyshev SIM Under a Perturbation of a Complex Line-Segment Spectrum."
Linear Algebra and Its Applications, 230: 47-60.
doi: 10.1016/0024-3795(93)00361-3 source: https://www.sciencedirect.com/science/article/pii/0024379593003613?via%3Dihub