I present enhanced R-matrix algorithms for analysis of general multilayered diffraction gratings. The previous R-matrix algorithms are enhanced in three aspects: computational efficiency, numerical stability, and application of half R-matrix in addition to full and quarter R-matrix recursions. On the basis of the eigensolutions of rigorous coupled-wave analysis, the enhanced R-matrix algorithms deal with eigen-submatrices directly and bypass the auxiliary layer R matrix. Such exclusion of a layer matrix leads to improvements in efficiency and algorithm robustness particularly for zero or small layer thickness relative to wavelength. Application of the enhanced algorithms to grating diffraction is exploited especially for the half and quarter R-matrix recursions. Comparison of various R-matrix algorithms via a table of flop counts shows that the enhanced algorithms are more efficient apart from being well conditioned.