[petsc-users] Solution of normal equations

[Alejandro Castro]

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.



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*[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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