[petsc-users] Solution of normal equations

[Mark Adams]

This matrix is SPD so you want to use -ksp_type cg

Without a matrix, preconditioning is hard. You can give it a shot. You need
to make a MatShell and use -pc_type none.

You will probably want to make a matrix and you should research solver
methods that have been used for problems like yours.

Mark

On Tue, Jul 19, 2022 at 12:07 PM Alejandro Castro
<alejandro.castro at tri.global> wrote:

> Hello PETSc users,
>
> I am looking to solve a (sparse) system of equations H⋅x=b where matrix H
> has the form H=D+Jᵀ⋅R⋅J, where both D and R are positive diagonal matrices.
> This is very similar to a set of normal equations, though not quite. J is
> square and most often with a large condition number κ(J) (and thus H's
> condition number will scale with the square of κ(J)).
>
> What method would you recommend for solving H⋅x=b? In particular, I
> imagine I do not want to form H directly. Also, what iterative method would
> you recommend given the large condition number?
>
> Thank you in advance,
>
> A.
>
>
>
> --
>
> *[image: Toyota Research Institute Logo]
> <https://www.tri.global/>Alejandro Castro (he/him)Manager, Dynamics &
> SimulationTOYOTA RESEARCH INSTITUTE <http://www.tri.global/>Los Altos
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