Linear Recurrence Equation Example. Fibonacci Sequence: f n = f n-1 +f n-2, with f 0 = 0, f 1 = 1 or Thus, computing f n is equivalent to computing using.

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Presentation transcript:

Linear Recurrence Equation Example. Fibonacci Sequence: f n = f n-1 +f n-2, with f 0 = 0, f 1 = 1 or Thus, computing f n is equivalent to computing using parallel prefix computation.

LU Decomposition of Tri-diagonal Matrix m i = e i / u i-1 (2 < i < n) (2 < i < n) How to solve? Special case of rational fraction

x i =(a, b, c, d) x i (a, b, c, d)  (a’, b’, c’, d’) ? Or, (a, b, c, d) (a’, b’, c’, d’) = (aa’+bc’, ab’+bd’, ca’+dc’, cb’+dd’) “ ” is associative. Thus, we can compute the operation.