We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a multivariate normal distribution whose covariance (precision) matrix can be decomposed as a positive-definite matrix minus (plus) a low-rank symmetric matrix. Example results illustrate the correctness and efficiency of the proposed simulation algorithms.
"Fast Simulation of Hyperplane-Truncated Multivariate Normal Distributions." Bayesian Anal. 12 (4) 1017 - 1037, December 2017. https://doi.org/10.1214/17-BA1052