Eigen SparseQR提供的结果与其他结果不同:bdcSVD,共轭梯度

问题描述

我尝试使用本征求解器(本征3.3.7)来求解线性系统Ax = b。但是,我发现SparseQR求解的结果(x)与密集求解器(bdcsvd)和其他稀疏求解器的结果不同,但是相对误差(|| Ax-b || / || b ||)相同。

有人可以帮助我理解sparseQR为什么给出不同的结果以及如何确保它得到的结果与SVD相同吗?

我还注意到,对于其他一些数据集,sparseQR和SVD给出的结果相同,但CG却不一样。

谢谢。

矩阵A和b可以在下面找到。


     0  35516      0  17732 -35516      0 -17732      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0
     0  17732      0  35516 -17732      0 -35516      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0
     0 -35516      0 -17732  35516      0  17732      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0
     0 -17732      0 -35516  17732      0  35516      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0
     0      0      0      0      0  35516      0  17732 -35516      0 -17732      0      0      0      0      0      0      0      0      0      0      0      0      0
     0      0      0      0      0  17732      0  35516 -17732      0 -35516      0      0      0      0      0      0      0      0      0      0      0      0      0
     0      0      0      0      0 -35516      0 -17732  35516      0  17732      0      0      0      0      0      0      0      0      0      0      0      0      0
     0      0      0      0      0 -17732      0 -35516  17732      0  35516      0      0      0      0      0      0      0      0      0      0      0      0      0
     0      0      0      0      0      0      0      0      0      0      0      0      0  35516      0  17732 -35516      0 -17732      0      0      0      0      0
     0      0      0      0      0      0      0      0      0      0      0      0      0  17732      0  35516 -17732      0 -35516      0      0      0      0      0
     0      0      0      0      0      0      0      0      0      0      0      0      0 -35516      0 -17732  35516      0  17732      0      0      0      0      0
     0      0      0      0      0      0      0      0      0      0      0      0      0 -17732      0 -35516  17732      0  35516      0      0      0      0      0
     0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0  35516      0  17732 -35516      0 -17732      0
     0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0  17732      0  35516 -17732      0 -35516      0
     0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0 -35516      0 -17732  35516      0  17732      0
     0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0 -17732      0 -35516  17732      0  35516      0
     0      0  35516  17732      0      0      0      0      0      0      0      0 -35516 -17732      0      0      0      0      0      0      0      0      0      0
     0      0  17732  35516      0      0      0      0      0      0      0      0 -17732 -35516      0      0      0      0      0      0      0      0      0      0
     0      0 -35516 -17732      0      0      0      0      0      0      0      0  35516  17732      0      0      0      0      0      0      0      0      0      0
     0      0 -17732 -35516      0      0      0      0      0      0      0      0  17732  35516      0      0      0      0      0      0      0      0      0      0
     0      0      0      0      0      0  35516  17732      0      0      0      0      0      0      0      0 -35516 -17732      0      0      0      0      0      0
     0      0      0      0      0      0  17732  35516      0      0      0      0      0      0      0      0 -17732 -35516      0      0      0      0      0      0
     0      0      0      0      0      0 -35516 -17732      0      0      0      0      0      0      0      0  35516  17732      0      0      0      0      0      0
     0      0      0      0      0      0 -17732 -35516      0      0      0      0      0      0      0      0  17732  35516      0      0      0      0      0      0
     0      0      0      0      0      0      0      0      0      0  35516  17732      0      0      0      0      0      0      0      0 -35516 -17732      0      0
     0      0      0      0      0      0      0      0      0      0  17732  35516      0      0      0      0      0      0      0      0 -17732 -35516      0      0
     0      0      0      0      0      0      0      0      0      0 -35516 -17732      0      0      0      0      0      0      0      0  35516  17732      0      0
     0      0      0      0      0      0      0      0      0      0 -17732 -35516      0      0      0      0      0      0      0      0  17732  35516      0      0


矩阵A:

      225915
     -380755
     -225915
      380755
 1.68807e+07
 9.48266e+06
-1.68807e+07
-9.48266e+06
    -32610.3
 -1.5961e+06
     32610.3
  1.5961e+06
-1.08558e+07
 1.41591e+06
 1.08558e+07
-1.41591e+06
-2.79489e+06
-4.57751e+06
 2.79489e+06
 4.57751e+06
 1.22018e+06
 3.70838e+06
-1.22018e+06
-3.70838e+06
-4.80155e+06
-2.53063e+06
 4.80155e+06
 2.53063e+06

b

style

解决方法

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