[petsc-users] How to set L1 norm as the converge test?

[Brian Yang]

Thanks everyone, I will try KSPSetConvergenceTest to test.

On Wed, Sep 24, 2014 at 2:54 PM, Jed Brown <jed at jedbrown.org> wrote:

> Matthew Knepley <knepley at gmail.com> writes:
>
> > On Wed, Sep 24, 2014 at 2:31 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >
> >>
> >>   Brian,
> >>
> >>     Your convergence test routine could call KSPBuildResidual() and then
> >> compute the 1-norm of the residual and make any decision it likes based
> on
> >> that norm.  See KSPSetConvergenceTest()
> >
> >
> > Note that what Barry is saying is that the convergence theory for CG
> > guarantees monotonicity in the energy (A) norm, but says nothing
> > about L1 so you might get crap.
>
> Moreover, if you have an overdetermined linear system, but want to
> minimize the 1-norm of the residual (instead of the 2-norm that least
> squares minimizes), you are actually asking to solve a "linear program"
> and need to use an LP solver (a very different algorithm).
>
> If you merely watch the 1-norm of the residual, it might increase as the
> least squares solver converges.
>



-- 
Brian Yang
U of Houston
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