In this paper, the efficient solution of the Fredholm integral
&lgr;u(y) + ∫ &Ggr; &kgr;(x,y) u(x) dsx = f(y), y∈ &Ggr;
is considered, where f is a (d-1)-dimensional manifold on &Ggr; ⊂ &RR; d. There are three common numerical techniques used to solve the equation, namely the Galerkin method, the collocation method, and the Nystrom method. These are applied based on the partition of the domain &Ggr; into triangles.The authors propose a purely algebraic algorithm, based on a collocation method for the generation of low-rank approximants from the matrix entries instead of kernels, that leads to improvement over existing computer codes. A new algorithm is also developed for matrix partitioning, to reduce the number of blocks generated.
