H-MATRIX METHODS FOR QUADRATIC INTEGRAL OPERATORS

In modelling of population dynamics we encounter with integral operator.Naive discretisation leads to full matrices and therefore to quadratic complexity O(n2), if n denotes the number of degrees of freedom .In a recent paper we have shown that it is possible to achieve a discretisation complexity of O(n).We introduce a numerical treatment for two popular kernel functions combining the ideas of H-matrices and the fast Fourier transformation (FFT). This leads to almost linear complexity of O(n log n) and O(n log2 n) but it turns unfortunately out that the new method is only applicable in a reasonable way for one of the two kernel functions .