Notebookverified
Half precision made the solver look converged
A residual plateau was mistaken for convergence after reduced precision erased the update direction.
Context
The goal was to reduce memory traffic in a batched conjugate-gradient solve by storing state in half precision.
Observation
The reported residual stopped changing, but a double-precision recomputation showed that the solution was not converged. The half-precision update direction had fallen below the representable scale of the accumulated state.
Next steps
Keep matrix products in reduced precision while accumulating the solution and residual norm in single precision. Treat a flat reported residual as a numerical warning rather than automatic convergence.