[petsc-users] BiCGSTAB for general use

[Jed Brown]

On Fri, Aug 12, 2011 at 12:26, Paul Anton Letnes <
paul.anton.letnes at gmail.com> wrote:

> I'm not 100% sure what you mean by "second kind integral operator", but it
> is a Fredholm equation of the first kind, as far as I understand (my
> background is physics rather than mathematics).


Is the thing you're trying to solve with actually of the first kind, not of
the second kind?

http://en.wikipedia.org/wiki/Fredholm_integral_equation

The distinction is whether there is essentially in whether there is a local
part to the equation or not. The issue, as I understand it, is that solving
a first-kind integral equation is generally not a stable process because the
eigenvalues of the integral operator decay to zero, implying that it is
essentially low rank, thus not invertible. Maybe you use some regularization
to get a system that is not essentially singular?
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