the errors from both effects, we introduce an additional parameter to the algorithm $p_d$, which decrements value of $q$, so that the actual value of $q$ that is used is $q' = \rm{max}(q - p_d, 0)$. This reduces the CPU and memory requirements of updating a given box, at the expense of increasing the errors due to truncating the Taylor terms.

### Parallelisation {#sec:parallelisation}

One interesting property of our approach is that affords an additional axis of parallelisation (the Taylor terms) in addition to those available for standard gridding (typically, data parallelisation over frequency channels). We assume that the parallelism is achieved through message passing.

In section \[sec:performance\] we show that the memory bandwidth and operations count for the FGT is dominated by updating the Taylor terms. As each of the Taylor terms is independent, one can in principle store each of the $(p-p_d + 1)^2$ Taylor terms on (up to) as many nodes, thereby dividing the per-node storage requirement by the number of nodes. For the case where $q'^2$ is a multiple of the number of nodes, the work is spread equally among the nodes. Each node can update its Taylor terms for the boxes within range, and, the 