New Efficient Algorithms with Positive Definite Radiosity Matrix
New efficient algorithms will be presented for solving diffuse radiosity problems, involving advantages of progressive radiosity. Demonstration of the algorithms and of their convergence relies on the new form of the radiosity equations, with a positive definite matrix. The methods have been tested with a new error formula, the (area-weighted) average relative error. The form with a symmetric, positive definite matrix penetrates into the gist of the radiosity problem deeper than the former radiosity or power variable equations. At the same time this makes it possible to apply several algorithms well-known from numerical analysis. In general, the positive definite form leads to algorithms, which are mathematically handleable, and of proven convergence and effectiveness.
KeywordsError Vector Positive Definite Matrix Average Relative Error Closed Environment Error Formula
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