arXiv:2610.07653v1 Announce Type: new Abstract: Recently, efficient sweep-based low-rank iterative solvers have been developed to reduce the computational costs of steady-state solves and implicit time integration of the radiative transfer equation (RTE). In particular, angular sampling based on the discrete empirical interpolation method (DEIM) or on error-indicated randomized greedy selection enables efficient, non-intrusive reuse of existing transport sweep implementations. However, randomized-greedy low-rank source iteration with diffusion synthetic acceleration (SI--DSA) enforces uniformly tight accuracy tolerances across all source iterations, thereby oversolving the early iterations, and it does not explicitly reuse angular bases from preceding iterations. More critically, like its full-rank counterpart, this approach may lose effectiveness in multiscale problems with strong material discontinuities. We address these limitations through two complementary developments. First, we introduce adaptive accuracy control into randomized-greedy low-rank SI--DSA, reducing intermediate ranks and computational cost while maintaining the accuracy required for convergence. A two-stage hybrid sampling strategy can provide further acceleration by switching to DEIM-based sampling near convergence, once the preceding angular basis becomes sufficiently representative. Second, we develop an inexact flexible GMRES--DSA solver for the integral scalar-flux reformulation, in which sweep-based low-rank approximations are confined to the construction of the right-hand side and the matrix--vector products. The scalar-flux Krylov basis is not compressed, thereby preserving Arnoldi orthogonality in exact arithmetic and allowing established inexact-GMRES analysis to guide adaptive accuracy control of low-rank operations. We present numerical results on benchmark problems that demonstrate the effectiveness of the proposed methods.