大型稀疏法方程组的代数多重网格解法

Algebraic Multigrid Solution of Large-Scale Sparse Normal Equatation

测量平差中经常会遇到大型稀疏法方程组的求解。传统的线性方程组迭代解法能够很快平滑误差分量中的高频分量;但对于低频分量衰减很慢。代数多重网格算法通过建立多重网格,并在不同的网格层上分别处理高低频误差分量,将所有层相互协调起来求解同一问题。这对于大规模稀疏线性方程组的求解,具有高效性。这里介绍了代数多重网格算法,并进行了改进,得到了AMG-CG算法。数值算例表明,代数多重网格算法(AMG)以及改进的AMG-CG算法对求解大型稀疏法方程组具有高效性和数值稳定性,改进后的AMG-CG算法在计算效率上进一步提高,对于大型稀疏法方程组的求解是可行有效的算法。

The solution of large-scale sparse normal equatation is often required in survey adjustment.The traditional iterative methods for linear systems can eliminate high frequency component of error component very quickly,but for low frequency component,it processes quite slowly.Algebraic multigrid method requests to establish multigrids,tackle high frequency component and low frequency component in different grid layers respectively and address the same question via coordinate all layers,which plays a high-efficient role in solving large-scale sparse normal equatation.Algebraic multigrid method was introduced and AMG-GG method was deduced by advancing the former.Numeric examples indicated that AMG method and advanced AMG-GG method were proved to be feasible and valid methods,and they were high-efficiency and stablity in solving large-scale sparse normal equatation.