A fast matrix-vector multiplication method for solving the radiosity equation

A “fast matrix–vector multiplication method” is proposed for iteratively solving discretizations of the radiosity equation (I −K)u = E. The method is illustrated by applying it to a discretization based on the centroid collocation method. A convergence analysis is given for this discretization, yielding a discretized linear system (I − Kn)un = En. The main contribution of the paper is the presentation of a fast method for evaluating multiplications Knv, avoiding the need to evaluate Kn explicitly and using fewer than O(n) operations. A detailed numerical example concludes the paper, and it illustrates that there is a large speedup when compared to a direct approach to discretization and solution of the radiosity equation. The paper is restricted to the surface S being unoccluded, a restriction to be removed in a later paper.