Numeric error propagation: Difference between revisions
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Although the example source file uses the F90 MODULE protocol, this is merely for convenience. Otherwise, there would be the same collection of routines, all sharing a COMMON work area. It would be easy enough to prepare an interactive calculator using this scheme so that different calculations (and data) could be more easily experimented with. Inspection might suggest a return to the laboratory in order to measure some factor with greater precision because its error proves to be the largest contributor to the spread in the result.
The trace as the calculation progresses shows a disconcerting surge in the intermediate values of the error estimate. One ought not "compute from the hip" and not worry over intermediate results that are not shown! More generally, the progression of error should be watched carefully lest assumptions prove invalid. For instance, ''at every step'' along the way, x → F(x), that x ± e is a ''small'' span, within which F(x) and F'(x) do not change greatly, still less pass a discontinuity. Seemingly helpful events such as F'(x) = 0 should be thought about... An alternative approach to F(x ± e) = F(x) ± |F'(x)|.e is to compute F(x - e) and F(x + e) as well as F(x). Some systems offer "interval arithmetic" that might assist with such a procedure, but they are not widely available.
===Fortran 90 ''et seq''.===
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