Linear Recurrence Equation

1
Linear Recurrence Equation
Example. Fibonacci Sequence fn fn-1 fn-2,
with f0 0, f1 1
or
Thus, computing fn is equivalent to
computing using parallel prefix computation.
2
LU Decomposition of Tri-diagonal Matrix
How to solve? Special case of rational fraction
mi ei / ui-1 (2 lt i lt n)
(2 lt i lt n)
3
xi(a, b, c, d) xi (a, b, c, d) ? (a, b, c,
d) ?
Or, (a, b, c, d) (a, b, c, d)
(aabc, abbd, cadc, cbdd)
is associative. Thus, we can compute the
operation.