Continued Fraction Interpolation

摘要

Interpolation by rational functions is especially useful for applications in which there are extended function ranges for abbreviated domains of definition. A particular case in point is the set of soil characteristic curves relating hydraulic conductivity, moisture content, and pressure head. In calculating the flow of fluids in unsaturated media, it is convenient to have values for both these curves and their derivatives. A relatively simple and accurate way to obtain both the curves and their derivatives from sparse data is via continued fraction interpolation. By defining the nth approximant F'/sub n/ of a continued fraction interpolant F/sub n/(x) = b sub 1 + H/sub n-1/(x), where H sub 1 - 1/b/sub n/; H/sub i/ = (x - x/sub n-1/)/(b/sub n-i+ H/sub i-1/); i = 2, ..., n-1; a very simple recursive for F'/sub n/(x) is derived as F/sub n/(x) = H'/sub n-1/. (ERA citation 09:027977)