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Advances in Computational Mathematics 12 (2000) 151174 151 A fast matrixvector multiplication method for solving the

Summary: Advances in Computational Mathematics 12 (2000) 151­174 151
A fast matrix­vector multiplication method for solving the
radiosity equation
Kendall Atkinson a, and David Da-Kwun Chien b
Department of Computer Science and Department of Mathematics, University of Iowa, Iowa City,
IA 52242, USA
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


Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa


Collections: Computer Technologies and Information Sciences