for the foreseeable future. Therefore, the performance of memory-bandwidth bound algorithms such as $w$-projection will not improve as quickly as an algorithm which is bound by arithmetic capacity. Furthermore, modern high performance computers rely on having a very large number of small nodes, with each node having relatively limited memory. The requirement to store large convolution functions is, therefore, at odds with having nodes with small amounts of memory.

Memory efficient algorithms, therefore, will be an important step on the path to implementing wide-field imaging capabilities for the Square Kilometre Array (SKA). We have embarked on an program to research new approaches to interferometric imaging, with particular emphasis on algorithms that align more closely with the memory-bound computing that will be available in the time frame of the SKA.

In this paper we describe a different approach to $w$-projection. The key to our method is to represent the convolution function, including the $w$-projection term, and an anti-aliasing function, as a complex Gaussian. The gridding and degridding problems can then be solved using the variable-width fast Gauss transform (FGT; @Strain91). One advantage of this approach is that it does not require convolution functions to be computed and stored, and the theoretical 