Abstract: The truncated version of the Minpert method—the IMinpert algorithm for large unsymmetric linear systems has been given in another paper. In order to accelerate the convergence rate of the IMinpert algorithm, the right preconditioning technique is used, and then the Flexible IMinpert algorithm（FIMinpert algorithm） is presented in this paper. The theoretical deduction and practical implementation issues of the FIMinpert algorithm are discussed in details. Numerical experiments show that the FIMinpert algorithm can achieve better convergence rate than the IMinpert algorithm and the GMRES algorithm.

Key words: unsymmetric linear systems, Krylov subspace methods, minimum joint backward perturbation, IMinpert algorithm, right preconditioning technique, incomplete orthogonalization process

摘要： 在Krylov子空间方法日益流行的今天，提出了又一求解大型稀疏线性方程组的Krylov子空间方法：灵活的IMinpert算法（即FIMinpert算法）。FIMinpert算法是在Minpert算法的截断版本即IMinpert算法的基础上结合右预处理技术，对原方程组作某些预处理来降低系数矩阵的条件数，从而大大加快迭代方法的收敛速度。给出了新算法的详细的理论推理过程和具体执行，并且通过数值实验表明，FIMinpert算法的收敛速度确实比IMinpert算法和GMRES算法快得多。

关键词: 非对称线性方程组, Krylov子空间方法, 最小联合向后扰动, IMinpert算法, 右预处理技术, 不完全正交化过程