matrix inversion

[Matthew Knepley]

On 9/21/07, Randall Mackie <randy at geosystem.us> wrote:
> Matt,
>
> There may be very valid reasons why one would want a matrix inverse,
> say in the context of solving optimizations where you need the
> inverse of the covariance matrix, and you need those values to
> embed in another system.

I do not agree. What are you going to do with the inverse that cannot be
done with LU? Backsolves against a matrix are commonplace.

  Matt

> In this case, just getting the action of the inverse times a vector
> is not what is needed.
>
> Randy
>
>
> Matthew Knepley wrote:
> > On 9/21/07, Randall Mackie <randy at geosystem.us> wrote:
> >> I have a collegue who is considering to use PETSc for programming
> >> his problem. He would like to know if you can get the actual
> >> inverse of a matrix, because this inverse is embedded in another
> >> larger system that is then solved.
> >>
> >> I suppose that if you solve the system directly, say with SuperLU
> >> or MUMPS, you could get the actual inverse? I looked briefly through
> >> the manual and documentation, but it didn't jump out at me.
> >
> > This makes several time this week people have asked for inverses. Never
> > never never use the inverse. Its not stable. The storage blows up. That is
> > why factorizations were invented. Numerical analysis courses have failed
> > the country entirely. Just use a KSP and tell it -ksp_type preonly -pc_type lu
> > and then you can customize the matrix type for different solvers. KSPSolve()
> > will apply the matrix. If you want to get the action on an entire matrix, this
> > is dense and we would have to put in the BLAS3 triangular solve calls.
> >
> >   Matt
> >
> >> Any advice here?
> >>
> >> Thanks, Randy
> >>
> >> --
> >> Randall Mackie
> >> GSY-USA, Inc.
> >> PMB# 643
> >> 2261 Market St.,
> >> San Francisco, CA 94114-1600
> >> Tel (415) 469-8649
> >> Fax (415) 469-5044
> >>
> >> California Registered Geophysicist
> >> License No. GP 1034
> >>
> >>
> >
> >
>
> --
> Randall Mackie
> GSY-USA, Inc.
> PMB# 643
> 2261 Market St.,
> San Francisco, CA 94114-1600
> Tel (415) 469-8649
> Fax (415) 469-5044
>
> California Registered Geophysicist
> License No. GP 1034
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
their experiments lead.
-- Norbert Wiener