On Monday, August 29, 2011 1:02:00 AM UTC-7, John Maddock wrote:
evaluate a polynomial approximation to the function: To consider a trivial example, if T*T isn't a T, then one can't even
result = A + B* T + C * T^2 + D * T^3...
to give a concrete example, the root finding algorithm that started this thread uses a polynomial approximation to the function to greatly speed up finding the root (we can find the polynomial approximation and it's root algebraically once we have evaluated enough points in the function). It's this insight that makes the algorithm converge so rapidly compared to the alternatives, but requiring that T*T != T breaks the underlying assumptions
not only in how it's implemented, but in how it actually works algorithmically.
The easy answer is that A, B, C and D are different types then. the types of A, B, C and D can be deduced from the type of T and the type of the result R, which are know at that point. Alfredo