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 <https://goo.gl/maps/3MF8fCYh8vV5YMHE6> / Cambridge <https://goo.gl/maps/9QWtf6NV6oNrdJih8>* -- Confidential or protected information may be contained in this email and/or attachment. Unless otherwise marked, all TRI email communications are considered "PROTECTED" and should not be shared or distributed. Thank you.
