[petsc-users] Regarding the conjugate gradient method

[Matthew Knepley]

On Thu, May 18, 2017 at 8:38 AM, Matt Baker <mbaker112 at outlook.de> wrote:

> Hello,
>
>
> just a quick question:
>
> The CG method is generally derived for spd matrices. However, the PETSc
> man page states
>
>
> Notes: The PCG method requires both the matrix and preconditioner to be
> symmetric positive (or negative) (semi) definite Only left preconditioning
> is supported.
>
>
> Does this mean CG works for semi-definite problems as well? Is that
> guaranteed then?
>
I believe that CG converges to A^+ b if b is in the range space of A, but I
would have to look it up. Its probably in Hestenes, "Optimization theory:
the finite dimensional case" 1975

  Thanks,

    Matt

> Thanks.
>



-- 
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
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