LU decomposition of the radiosity matrix

Abstract

Lighting calculations involving iteration or repetition present a problem of interest for many lighting tasks. Repeated calculation is needed, for example, in a design process for the best design evaluation or when a lighting system performance simulation is required A fast solution of the repeated calculation problem can be of special value for the computer-aided design of a lighting system. This paper discusses how the problem of repeated lighting calculations could be handled by the LU decomposition method. This method is commonly used by numerical mathematics for the solution of a single system of linear equations Ax = b, when there is more than one light-hand side b. To speed up the process of repeated solutions, the method involves decomposing a matrix A into an equivalent pair L and U, where L and U are lower and upper triangular matrices, respectively. The proposed LU decomposition method is compared with the traditional solution methods and its performance is shown. Examples of its use are presented to illustrate a possible field for the application of the method.