Re: Regarding Gsoc project

[Kai Torben Ohlhus]

On Sun, Mar 2, 2014 at 7:04 AM, vaibhav gupta <address@hidden> wrote:

Hello Kai,

I have read the book given by you.Now I have some idea of what is incomplete factorization,how we divide a matrix into upper and lower triangular matrix,ILU(0) factorization.

But i couldn't understand what is level of fill and ILU(p) ?

Kindly guide me further.

Thanks And Regards

Vaibhav

 

Hi Vaibhav,

Loosely speaking, during the Gaussian Elimination columns tend to get filled by small values. This is bad if you want to keep a sparse matrix sparse. In order to keep the sparsity for the incomplete factorization ILU(0) says, do only update the already existing pattern of the original matrix. ILU(1) says, add maximal one element per column/row. ILU(2) means 2, .... Assume your square sparse matrix A has dimension n, then ILU(n) would result in a complete LU-factorization. A more precise definition is given in Saads book [1] Chapter 10.3.3. The comparison of the pictures 10.2 and 10.3 should emphasize the meaning of level-of-fill.

Again I remind you to follow the bottom-posting style [2] for this mailing list, as this makes it easier to follow our conversation.

Best,
Kai

[1] http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf
[2] http://en.wikipedia.org/wiki/Posting_style#Bottom-posting