MATLAB中大型线性方程组的非定常迭代法

Nonstationary Iterative Methods for Large Linear Systems in MATLAB

科学研究和大型工程设计中很多问题以非线性数学模型来描述,而这些数学模型求解常常归结为各种大型线性方程组的求解,因而能否有效地求解大型线性方程组,特别是病态的方程组,是非常关键的.本文介绍了MATLAB中求解大型线性方程组常用的非定常迭代法,并以GMRES算法为例介绍了算法的数学描述.

Lots of problems are defined by nonlinear mathematic model in scientific research and large technological (design). Thus extracting solution of these models lead to solving the large linear systems. Therefore, whether the large (linear) systems, especially ill-posed equations, can be effectively solved is very important. Some nonstationary Iterative methods for large linear systems in MATLAB are introduced in this paper. We also introduce the mathematic description of the GMRES method.