[petsc-dev] How do you get RIchardson?

[Sean Farley]

>
> If one defines a Picard method as any fixed-point iteration then x^{n+1} =
>> x^{n} - J(x^{n})^{-1} F(x^{n}) is a Picard iteration for the equation x = x
>> - J(x)^{-1} F(x) in other words Newtons' method is a Picard method; is this
>> true? Is Picard algorithm a synonym for fixed point iteration?
>>
>
> http://en.wikipedia.org/wiki/Picard_iteration (redirects to "Fixed point
> iteration")
>
> Also, Tim Kelley's book describes "fixed point iteration" as "also called
> nonlinear Richardson iteration, Picard iteration, or the method of
> successive substitution".
>

Actually, the first (in recorded history, of course) version of fixed point
iteration "originated in antiquity, appearing, for example, in the writings
of Heron of Alexandria [1]." Perhaps, we should, in the interest of not
being historically blind, call it the Heron method.

[1] E. T. Bell. The Development of Mathematics. Second ed. McGraw-Hill, New
York 1945.
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