Is a Chebyshev Method Optimal for an Elliptic Region also Optimal for a Nearly Elliptic Region?
Linear Algebra and Its Applications
The asymptotic rate of convergence of an optimal Chebyshev semiiterative method for solving a real and nonsymmetric linear system x=Tx+c can be improved by the related (2,2)-step iterative methods under certain conditions. The condition for which a Chebyshev method asymptotically optimal for an elliptic region is also asymptotically optimal for a nearly elliptic region is presented. Thus a (2,2)-step method is asymptotically superior to the Chebyshev method asymtotically optimal for a nearly elliptic region under certain conditions. A numerical example illustrates our results.
"Is a Chebyshev Method Optimal for an Elliptic Region also Optimal for a Nearly Elliptic Region?."
Linear Algebra and Its Applications, 338 (1-3): 37-51.
doi: 10.1016/S0024-3795(01)00362-7 source: https://www.sciencedirect.com/science/article/pii/S0024379501003627?via%3Dihub