Solving Ax = b with a minimized x l2 norm

[doun...@student.liu.se]

Hi,

I am currently doing my master thesis on The University of Linköping (Sweden). I wish to create a direction field that is describing a mesh, very common to what this paper describes:

http://www.cs.columbia.edu/~keenan/Projects/TrivialConnections/paper.pdf

What I've come down to now is that I've got my self a linear system Ax = b, where I want to find x. Also for a proper solution I wish to find the minimum ||x|| that solves the problem. Right now I've tried the ceres solver using cost functions that returns residuals in a simple manner, something like this: 

residual = |(Ax - b)| + |x|

But it havent given me any decent results yet. So far I usually end up with a vector x containing zeroes (which doesnt solve the system Ax = b). 

When googling around I get the impression that this is a common problem in mathematics. So if anyone have done similar things, such as solving linear systems and/or minimizing vectors and got some words of advice it would be most appreciated!

//Douglas

[doun...@student.liu.se]

Forgot to mention:

A is a underconstrained sparse matrix. i.e. there is more than one solution to the Ax = b problem!

[Sameer Agarwal]

Douglas you do not need ceres to solve this problem. You should use a linear least squares solver. E.g. you can use suitesparseqr to solve your problem easily and in one step.
Sameer

On Oct 25, 2013 1:29 AM, <doun...@student.liu.se> wrote:

Forgot to mention:

A is a underconstrained sparse matrix. i.e. there is more than one solution to the Ax = b problem!

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[Douglas Nordwall]

Im sitting on a windows system and having a bad time trying to build SuitesparseQR. Do you know any other libraries (preferably supported for windows) that you could recommend for solving this problem?

//Douglas

[Jon Simpkins]

For a linear least-squares solution, Eigen might be a good alternative. Great library, and easy to use.

Also, these might be some good notes on the problem it seems like you're working on.

Best,

-Jon

On Wed, Oct 30, 2013 at 5:19 AM, Douglas Nordwall <doun...@student.liu.se> wrote:

Im sitting on a windows system and having a bad time trying to build SuitesparseQR. Do you know any other libraries (preferably supported for windows) that you could recommend for solving this problem?

//Douglas

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