An Adaptive Strategy of Improving Convergence of IDR(s)-Jacobi Method

The conventional Jacobi method is well known to be a simple one of stationary iterative methods for solving a linear system of equations, but it converges slowly and lacks of robustness of convergence. Therefore, we improve this Jacobi method by means of Induced Dimension Reduction (IDR) Theorem proposed by Sonneveld et al. in 2008 in order to gain robustness of convergence. That is, we devise the IDR-based Jacobi method with relaxed parameter ωn and its adaptive and cyclically adaptive tuning. Many numerical experiments verifies effectiveness and robustness of the IDR-based Jacobi methods. Characteristics of convergence of some IDR-based Jacobi methods may be useful for a variety of analysis in the field of applications