[petsc-users] Condition number of a matrix

Jed Brown jedbrown at mcs.anl.gov
Thu Oct 3 21:25:11 CDT 2013

Qiyue Lu <luqiyue at hotmail.com> writes:

> Dear All:
> I am solving a linear system Ax=b with about 40 millions DOF in PETSc. The solver is CR/Bjacobi. The driver is modified from source code : 
> petsc-3.3-p6/src/ksp/ksp/examples/tutorials/ex10.c 
> I am expecting the condition number of matrix A can be included in the output file but it doesn't now. I am wondering, is there any function or option eligible to print its condition number? thanks. 

Computing an accurate condition number is more expensive than solving a
linear system.  Your best bet if you need an accurate condition number
is to use SLEPc to compute the largest and smallest values.

When using GMRES or CG, you can use -ksp_monitor_singular_value to get
estimates of the largest and smallest singular values of the
*preconditioned* operator.  For large problems, this approach converges
too slowly without preconditioning to be useful for estimating the
extrema of the unpreconditioned operator.
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