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We present a new algorithm for computing the quasi-stationary distribution ofsubcritical Galton--Watson branching processes. This algorithm is based on aparticular discretization of a well-known functional equation thatcharacterizes the quasi-stationary distribution of these processes. We providea theoretical analysis of the approximate low-rank structure that stems fromthis discretization, and we extend the procedure to multitype branchingprocesses. We use numerical examples to demonstrate that our algorithm is bothmore accurate and more efficient than other approaches.

A low-rank technique for computing the quasi-stationary distribution of subcritical Galton-Watson processes