[Trilinos-Users] Ifpack preconditioner question

[Alicia M Klinvex]

Hello,

I'm trying to find the eigenvalues of a matrix from the Tim Davis collection (n~1.5 million, SPD, infinity norm~1e8, condition number unknown).  I generated a preconditioner using Ifpack to use with the eigensolver and got the following output:

================================================================================
Ifpack_ILUT: IFPACK ILUT (fill=1.05, relax=0, athr=1e-06, rthr=1, droptol=1e-12)

Level-of-fill      = 1.05
Absolute threshold = 1e-06
Relative threshold = 1
Relax value        = 0
Condition number estimate       = 8.58419e-05
Global number of rows           = 1564794
Number of nonzeros in A         = 114165372
Number of nonzeros in L + U     = 2969149 ( = 2.60074 % of A)
nonzeros / rows                 = 75.8985

Phase           # calls   Total Time (s)       Total MFlops     MFlops/s
-----           -------   --------------       ------------     --------
Initialize()        1      4.05312e-06               0.0            0.0
Compute()           1          34.8147                0                0
ApplyInverse()      1         0.039957                0                0
================================================================================

I have a few questions about this output:
1.  Why is the condition number estimate less than 1?
2.  Why is the number of nonzeros in L + U so low?  Does it have to do with the droptol?

As always, code is available on request.  Thank you for your help!

- Alicia