[petsc-users] Is there efficeint method for matrix with one extremely small eigen value?

[Umut Tabak]

On 04/06/2011 04:32 PM, Jed Brown wrote:
> On Wed, 6 Apr 2011 22:24:50 +0800 (CST), "Gong Ding"<gdiso at ustc.edu>  wrote:
>    
>> Hi,
>> Can some one gives me advise on how to solve the ill conditioned problem
>> efficiently with iterative method (since the problem size is big).
>>
>> I calculated the smallest eigen values as well as the largest eigen values.
>> There exist one extremely small eigen value, which made the system ill conditioned.
>> I guess method such as Tikhonov regularization may work?
>> Or there are some cheaper method works, if I can endure some inaccuracy in the solution.
>>
>>
>> Smallest 0 eigen value: -2.112144e-15 with error 9.452618e-14
>>      
> Your problem has a null space of dimension 1. Determine the eigenvector associated with this eigenvalue. That is the null space, it might just be a constant. Create a MatNullSpace and use KSPSetNullSpace(). (If it is the constant, you can just use -ksp_constant_null_space.) See the section in the users manual on solving singular systems.
>    
Just curious, are not the other negative eigenvalues problematic as well?