 
Summary: Advances in Computational Mathematics 12 (2000) 151174 151
A fast matrixvector multiplication method for solving the
radiosity equation
Kendall Atkinson a, and David DaKwun Chien b
a
Department of Computer Science and Department of Mathematics, University of Iowa, Iowa City,
IA 52242, USA
b
Department of Mathematics, California State University San Marcos, San Marcos, CA 92096, USA
Received September 1998; revised September 1999
Communicated by I. Sloan
A "fast matrixvector multiplication method" is proposed for iteratively solving dis
cretizations 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 multi
plications Knv, avoiding the need to evaluate Kn explicitly and using fewer than O(n2
)
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
