CG, SYMMLQ, and MINRES are Krylov subspace methods for solving large
symmetric systems of linear equations. CG (the conjugate-gradient method) is
reliable on positive-definite systems, while SYMMLQ and MINRES are designed for
indefinite systems. When these methods are applied to an incompatible system
(that is, a singular symmetric least-squares problem), CG could break down and
SYMMLQ's solution could explode, while MINRES would give a least-squares
solution but not necessarily the minimum-length solution (often called the
pseudoinverse solution).