Approximation of boundary element matrices

This article considers the problem of approximating a general asymptoticall y smooth function in two variables, typically arising in integral formulati ons of boundary value problems, by a sum of products of two functions in on e variable. From these results an iterative algorithm for the low-rank appr oximation of blocks of large unstructured matrices generated by asymptotica lly smooth functions is developed. This algorithm uses only few entries fro m the original block and since it has a natural stopping criterion the appr oximative rank is not needed in advance.