The Self-Adaptive Multi-Splitting Parallel Methods for Non-Hermitian Positive Definite Systems

摘要

We present the convergent splitting and convergent multisplirting for linear system of algebraic equations Ax = b when the coefficient matrix is a non-hermitian positive definite matrix. Furthermore, we also establish the comparison theorems of different splittings or multisplittings based on numerical radius. Mainly, we propose two new self-adaptive multisplitting parallel methods which the weighting matrices are self-adaptive. Finally, we give an application to solve the two- dimensional advection-diffusion equations.