[petsc-dev] How do you get RIchardson?

[Matthew Knepley]

On Fri, Sep 16, 2011 at 5:28 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Sat, Sep 17, 2011 at 00:20, Matthew Knepley <knepley at gmail.com> wrote:
>
>> My definition is in no way a "strict" subset. Define your nonlinear
>> operator to have a solve, and it has what you want.
>
>
> You want to solve
>
> f(x) = 0
>
> but you have to write
>
> x = g(x)
>
> to apply a fixed point method. So you do, e.g.
>
> x = A(x)^{-1} b
>
> Now we have to come up with a nonlinear problem f(x) = 0 such that
>
> x = x - f(x) = A(x)^{-1} b
>
> Evidently that is f(x) = x - A(x)^{-1} b. Now I have this extra x floating
> around just so it can be subtracted. Just because you can transform
> something to make a certain choice general doesn't make it so.
>

It most certainly does make it so. You can definitely, in user code, define
an F that produces the iteration that you
want. You cannot write a Newton that does what I want. How hard is that to
understand? It is not hard, in fact, but
this is arguing for the sake of not being wrong.

   Matt

-- 
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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