The numerical calculation of traditional coherent-mode representations (CMRs) involves an eigenvalue decomposition of the cross-spectral density matrix. An efficient alternative modal representation of a partially coherent field can be realized using an LDL decomposition. Storage requirements are reduced by an amount on the order of the ratio between the coherence length and the source width. The efficiency of calculations requiring a CMR (e.g., numerical evaluation of partially coherent propagation effects) may thus be significantly improved, particularly when low-coherence fields are considered.