I submitted a PR #16202 to introduce the Symmetric LQ (SYMMLQ) method in SciPy and fix the user's issue #13537. The PR website is as follows: https://github.com/scipy/scipy/pull/16202 Just like Minimal Residual method (MINRES), the SYMMLQ is also a key and important Krylov subspace method for symmetric indefinite systems, which was originally proposed by C.C.Paige and M.A.Saunders (cited by 2283 in Google) and widely used in some well-known math libraries such as MATLAB, PETSc, Trilinos and PyKrylov mentioned in the issue #13537. SYMMLQ is a variant of Conjugate Gradient method (CG). For symmetric positive-definite problems, SYMMLQ and CG has same convergence, but for symmetric indefinite problems, SYMMLQ has a smoother convergence curve than CG (CG is easier to diverge), its test results are shown in `Additional Information` of #16202. This PR is a python translation of PETSc implementation (It has been cited in `References` of `symmlq.py`) and some changes have been made based on the operation features of NumPy/SciPy. If anyone is interested in this PR, please feel free to help review it. Hope you like it, thanks.
Best Regards, Gang