On the convergence of monoparametric k-step iterative euler methods for the solution of linear systems

Abstract

For the solution of the nonsingular linear system x = Tx+c, two monoparametric stationary k—step iterative methods are considered. By using Euler transforms and for various values of their parameter ω the two methods are analyzed and studied as regards: (i) Their (optimum) convergence for a given configuration of the spectrum σ(T) of T and (ii) Their region of convergence R _k , for a permissible ω, for all T's for which σ(T) ⊂ R _k . Answers to both questions are given and it is shown that if the two methods share the same quantity ρ, defined in the paper, the optimum second method is asymptotically much faster than the optimum first one.

Keywords:

• k-step Iterative Euler Methods
• asymptotic convergence factor

C.R. Categories:

• 5.1.4