Would there ever be a case that we want ||K|| > 1 in real life examples? I wonder if there exists anywhere in simulation that makes energy increases as it goes.
That would just blow up though. Maybe the whole scene would just be rendered max brightness.
I think fundamentally if ||K|| > 1 this violates conservation of energy in some sense. It's implying that after one bounce there somehow is more brightness in the scene even despite any light that is absorbed into the materials into the scene.
If ||K|| < 1, K is called a contraction operator.
Assume ||K|| < 1, I understand that numerically the equation would converge to some final value. But imagine the case where there are two mirrors facing each other, the light would just keep bouncing back and forth. Intuitively this would go on forever with non-decreasing value, but it doesn't seem so since the value should eventually converge. Am I missing anything?