Re: [eigen] Another LDLt issue

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

I see. So we can always provide general selfadjoint LDLt "at the
user's own risk". The generic case is that it will "work" since
division by exactly 0 would be incredibly bad luck, but it will be
unstable because one will be dividing by small numbers.

It might be useful for solving / inversion, but then it will be in
hard competition against partial-pivoting block LU that i want to
implement "real soon now". So I'm not completely sure it will find
much use.

You say:

> for symmetric, non-positive definite matrices without pivoting.

But the problem is that pivoting won't help here if all the remaining
diagonal coefficients are zero. Indeed, a meaningful pivoting LDLt is
of the form:

PLDLtPt

In other words, the two permutations involved are adjoint of each
other. The reason for this requirement is that we need to preserve
self-adjointness.

Cheers,
Benoit