You can think of radiosity rendering as something like seeking the first eigenvalue of a transformation matrix; each vector element identifies the luminous flux at a particular point in space oriented in a particular direction. The transformation matrix identifies the transformation function of this six-dimensional light field as it propagates through space and bounces off objects, along with whatever sources of illumination are needed. This vector must necessarily be of very high dimensionality in order to provide a reasonable approximation, but it may be possible to do a reasonable job by subdividing space and directionality recursively using interval arithmetic until you reach an adequate approximation.