求解大型非对称线性方程组的拟最小残量IOM（q）算法

不完全正交化算法（IOM（q））由于存储量和计算量小，常用来求解大非对称线性方程组。而此方法收敛过程常出现不规划振荡现象，从而影响了收敛速度。本文将拟残量最小的化性质加到IMO（q）算法中，提出拟最小残量不完全正交化算法（QMRIOM（q），这样收敛曲线光滑无振荡，从而大大加快其收敛速度，而且保留其存储量和计算量小的性质。

A Quasi-Minimal Residual IOM(q) Method for Solving Large Unsymmetric Linear Systems

The incomplete orthogonalization methods(IOM(q)), for its less storage and computing cost, have been used for solving large unsymmetric linear systems. However, the IOM(q) exhibites irregular convergence behavior with wild oscillations in the residual norms though it tends to decrease in a very slow manner. This paper proposes a novel quasi minimal residual incomplete orthogonalization method (QMRIOM(q)). Numerical experiments show that it has smoothy convergence behavior and is more effective, especially when using its restarted version. The convergence can be much faster, and the less storage and computing cost property is retained.