稀疏矩阵超线性方程组c/c ++库 [英] sparse matrix overdetermined linear equation system c/c++ library

问题描述

我需要一个库来解决Ax = b系统，其中A是一个非对称的稀疏矩阵，每行有8个条目(而且可能很大).我认为实现双共轭梯度的库应该不错，但我找不到能起作用的库(我尝试过iml ++，但是iml ++/sparselib ++包中缺少一些标头).有提示吗?

I need a library to solve Ax=b systems, where A is a non-symmetric sparse matrix, with 8 entry per row (and it might be quite big). I think a library that implements biconjugate gradient should be fine, but i can't find one that works (i've tried iml++, but there are some headers missing in the iml++/sparselib++ packages). Any tips?

推荐答案

有处理超定系统的标准方法.例如，维基百科这样说:

There are standard ways of treating overdetermined systems. For example Wikipedia says this:

一组线性联立方程可以矩阵形式表示为Ax = y.如果方程比变量多，则称该系统为超定的，(通常)没有解.然后可以将系统更改为(A ^T A)x = A ^T y.新系统具有与变量一样多的方程(矩阵A ^T A是方矩阵)，可以用通常的方法求解.该解决方案是原始超定系统的最小二乘解，它使欧几里得范数|| Ax-y ||最小化，该度量是原始系统两侧之间的差异的度量.

A set of linear simultaneous equations can be written in matrix form as Ax = y. If there are more equations than variables, the system is called overdetermined, and has (in general) no solutions. The system can then be changed to (A^TA)x = A^Ty. The new system has as many equations as variables (the matrix A^TA is a square matrix) and can be solved in the usual way. The solution is a least-squares solution of the original, overdetermined system, minimizing the Euclidean norm ||Ax − y||, a measure of the discrepancy between the two sides in the original system.

因此，您可以使用任何标准的方矩阵稀疏求解器.

Therefore you can use any standard square matrix sparse solver.

我个人使用Tim Davis的 CSparse 中的直接求解器.蒂姆写了许多出色的直接稀疏求解器.实际上，他的 UMFPACK 是另一个很好的选择，例如，MATLAB已将其使用. .请注意，这两个求解器均提供C接口.如果您正在寻找具有本机C ++接口的功能，那么我无能为力.

Personally I use a direct solver from CSparse by Tim Davis. Tim has written a number of excellent direct sparse solvers. Indeed, his UMFPACK is another excellent option and is used by MATLAB, for example. Note that both of these solvers offer C interfaces. If you are looking for something with a native C++ interface then I have nothing to offer.

我在迭代求解器方面有一些经验.但是，我发现对于所要解决的问题，对于大型矩阵而言，迭代方法变得不稳定.我在直接求解器上取得了更大的成功.当然，根据问题抛出的矩阵类型，您可能会有相反的经验.

I have had some experience with iterative solvers. However, I have found that for the problems I was looking at, the iterative methods became unstable for large matrices. I have had much more success with direct solvers. Of course, it's perfectly plausible that you could have the reverse experience depending on the type of matrix your problem throws up.

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