What's the most efficient way to solve a sparse linear system Ax = b?

77 次查看（过去 30 天）
JUNWEI ZHANG
JUNWEI ZHANG 2017-8-7
回答： Jess 2018-8-15
In my project I have to solve an over-determined linear system Ax = b, where A is a large and sparse non-square matrix. We've explored A to have the following structural properties:
As can be seen above, A can be divided into two parts: the left part is a block diagonal matrix, which is ideal for solving linear systems. However the right part is a concatenation of several block diagonal matrices, which complicated to problem.
We've studied this structure for weeks but hasn't found an efficient solver that recognizes this structure. So far the best way to solve this is by sparse(A) \ b, which is way faster than pinv(A)*b or simply A\b. We believe there is still room for improvement because now only sparsity is exploited, not the structure.
Does anyone have any advice on how to solve this linear system more efficiently? BTW, what's the computational complexity for sparse(A) \ b?
Thanks in advance!

请先登录，再回答此问题。

回答（2 个）

KSSV
KSSV 2017-8-7
编辑：KSSV 2017-8-7
If you have GPU, you may consider using mldivide which is same as A\B..and might be faster. YOu can read it here, how the \ works:
http://in.mathworks.com/help/matlab/ref/mldivide.html
Jess
Jess 2018-8-15
There are very few cases where the `\` operator isn't the fastest and roughly the most accurate. I've done a lot of testing of this against other algorithms and packages in the numerical science community. It's really top-notch for almost all cases. For the cases that it wasn't great, it usually had slightly less accuracy than other methods.

类别

在 Help Center 和 File Exchange 中查找有关 Operating on Diagonal Matrices 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by