[petsc-dev] How do you get RIchardson?

[Matthew Knepley]

On Fri, Sep 16, 2011 at 3:58 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Fri, Sep 16, 2011 at 22:42, Matthew Knepley <knepley at gmail.com> wrote:
>
>> It is of course a fixed point iteration, and your definition of Picard is
>> a classic logical
>> fallacy. This is a valid fixed point iteration, Picard refers to a fixed
>> point iteration,
>> therefore all Picard iterations are of this form. In fact, Picard
>> encompasses fixed
>> point iteration to solve nonlinear equations.
>>
>
> I did not assert that it was the _only_ Picard, merely that it is the
> Picard used in practice to solve nonlinear differential equations. In naming
> SNESPICARD, you made a different choice, at least as valid in mathematical
> purity, but not the fixed point iteration commonly used to solve nonlinear
> differential equations. I don't understand why you are so enamored with that
> name.
>

It is the name for this generic concept:

  Solve F(u) = 0, by successive approximations u^{n+1} = F(u^n)

There is no other name for this process, and the proper name is the Picard
Iteration. I do not know why
you have such a hard time with historically accurate naming.

    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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