Convergence theory for orthogonal cycling probes

Investigate the convergence and theoretical guarantees of the PISO and PISO variants using orthogonal cycling probe directions whose successive probes are dependent and therefore fall outside the independent-probe assumptions of the current analysis.

Background

The experiments include empirically strong orthogonal cycling variants of PISO and PISO. These variants cycle through the columns of a random orthonormal frame, producing a spherical one-step marginal but dependence across consecutive iterations.

The stated theory assumes independently sampled probe directions, so it does not cover the observed cycling behavior. The conclusion explicitly identifies analysis of these dependent probes as unresolved.