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petsc_solver shows that krylov solver works without attaching the nullspace
as the rhs is orthogonalized

scipy_solver uses krylov solver without nullspace - works only with b \perp Z.
Also illustrates that (1-ZZ^t)A has no effect one the solution but the system
matrix is then significantly denser.

the above statements are true if x0, the intial guess for KrylovSolver is such
that ZZ^Tx0 = 0. In case x0 has some component in the nullspace, nullspace info
must be attached to krylov solver otherwise divergence. Petsc krylov solver
with nullspace + AMG preconditioner with x0, ZZ^T x0 !=0, converges but the
solution is wrong, even if the preconditioner as well as A are aware of the
nullspace!

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Playig around with Krylov solvers

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