A fast collocation method for the radiosity equation, based on the hierarchical algorithm of Hanrahan and Salzman: the 1d case

Abstract

In this paper we study a collocation method with piecewise constant trial functions for the solution of the planar radiosity equation. The matrix of the collocation method is approximated by a method which was developed by Hanrahan et al. [9,10]. We prove that the modified collocation method results in a reduction of work while the order of convergence stays the same. Numerical examples demonstrate the theoretical results.