Eigen-analysis for Radiosity Systems

The convergence of iterative methods used to solve the linear equations arising from radiosity systems depends on the distribution of the eigenvalues of the radiosity coefficient matrix. In this paper we prove that all eigenvalues of the radiosity coefficient matrix are real and positive. This fact may allow us to obtain fast radiosity solutions using the knowledge about the spectrum of the matrix. Moreover, the physical meaning of the eigenvectors in global illumination applications is an open problem in graphics. In order to contribute to the clarification of this question, we present some experiments based on the theory of matrices, in which we show interesting features that arise when the eigenvectors are used as solution vectors in graphics settings.