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Instead, the equation can more readily be solved iteratively, by repeatedly applying the single-bounce update formula above.

Formally, this is a solution of the matrix equation by Jacobi iteration.

Because the reflectivities ρ < sub > i </ sub > are less than 1, this scheme converges quickly, typically requiring only a handful of iterations to produce a reasonable solution.

Other standard iterative methods for matrix equation solutions can also be used, for example the Gauss – Seidel method, where updated values for each patch are used in the calculation as soon as they are computed, rather than all being updated synchronously at the end of each sweep.

The solution can also be tweaked to iterate over each of the sending elements in turn in its main outermost loop for each update, rather than each of the receiving patches.

This is known as the shooting variant of the algorithm, as opposed to the gathering variant.

Using the view factor reciprocity, A < sub > i </ sub > F < sub > ij </ sub > = A < sub > j </ sub > F < sub > ji </ sub >, the update equation can also be re-written in terms of the view factor F < sub > ji </ sub > seen by each sending patch A < sub > j </ sub >: