中文摘要：

采用基于矩阵图集的粗化算法形成粗点集,构造改进的插值算子,结合V型多重网格法和瀑布型多重网格法的算法结构,提出了一种改进的代数多重网格（IAMG）法,并估计了该算法的计算量。将IAMG法运用于求解牛顿算法中线性校正方程,提出了求解非线性椭圆型问题的非精确牛顿代数多重网格（IN-AMG）法。数值实验表明与对比算法相比,IN-AMG法在求解线性校正方程方面的整体计算量更少、计算时间更短。

英文摘要：

A new interpolation operator is designed by combining with the coarse grid points, which are given by using the coarsening algorithm based on the graph of the stiffness matrix. An improved algebraic multigrid （IAMG） method is presented for linear equa-tions, by combining with the structure of V-cycle multigrid method and eascadie multigrid method. The calculation of the IAMG al-gorithm is estimated. And the algorithm is used in solving the linear correction equation of Newton algorithm. Then inexact Newton algebraic multigrid （IN-AMG） method is proposed for nonlinear elliptic problem. The numerical experiment shows that the IN-AMG method can decrease amount of calculation and reduce the computation time greatly, compared with the contrast algorithm.