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- JOHN H. HALTON
- 1992

Given a linear system Ax = b, where x is an m-vector, direct numerical methods, such as Gaussian elimination, take time O(m 3) to find x. Iterative numerical methods, such as the Gauss-Seidel method or SOR, reduce the system to the form x = a + Hx, whence x = ∑r=0 ∞ ּ H r a; and then apply the iterations x 0 = a, x s+1 = a + Hx s , until sufficient accuracy… (More)

In this paper we extend the reuse of paths to the shot from a moving light source. In the classical algorithm new paths have to be cast from each new position of a light source. We show that we can reuse all paths for all positions, obtaining in this way a theoretical maximum speed-up equal to the average length of the shooting path.

- JOHN H. HALTON
- 2010