Solving large linear system of Ax=b while A is a non-square Matrix?

Hi,

I was using gmres to solve linear sysmtem Ax=b where A is a n*n large square matrix and b is n*1.

However, if A is m*n matrix where m>n that is least square case than can we use some iterative method like gmres (Generalized minimum residual method) or pcg (Preconditioned conjugate gradients method) type approach to solve it faster like for square case.

The basic goal is to solve large non-square matrix A faster for x.

Please help me with the matlab functions that handle this case?

Thanks

[Walter Roberson]

\ operator handles this case. I do not recall at the moment what it calls for this case; qr() I think.

[ZR]

Thanks for the feedback.

Yes this method is working and i can compute solution.

However, i was thinking about the convergence of solution and accuracy?

Is it the same as we have in GMRES method?

[Matt J]

Probably more accurate than GMRES, because it is non-iterative.

[ZR]

I have also test the matlab operator lsqlin() which is even faster than qr().

However, still i feel a more faster operator will be available compare to lsqlin that can solve large matrix A for x.

[ZR]

Although i can solve non-sqaure A matrix using operator qr() but it is not fast as we observe in case of gmres for square matrix A.

Answer 1

[Matt J]

In addition to mldivide, as suggested by Walter, you could pre-multiply your equation by A.' to obtain the square symmetric system

(A.'*A)*x=A.'*b

and then use pcg or gmres as before. PCG might be preferable, because the conditioning of the above system is poorer than for the original system A*x=b.