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on 11/21/2014 4:00 PM
A while back I came upon a seemingly not-too-difficult programming exercise: Define a recurrence $$x_n$$ by $$f(y, z) = 108 - \frac{815 - 1500/z}{y}$$ $$x_0 = 4$$ $$x_1 = 4.25$$ $$x_i = f(x_{i-1}, x_{i-2})$$ Compute $$x_{30}$$. This isn’t too hard to code up, using perhaps a recursive function to represent $$x_i$$. With normal double-precision floats, as $$i$$ increases, the result converges neatly toward 100. Super! Unfortunately, 100 is not even close to the right answer. This recurrence actually [...]