For a concrete illustration, examine a segment from the Abramowitz and Stegun (A&S) tables of natural logarithms. Here, h = 10−3. Linear interpolation yields an error proportional to h², or about 10−6. Since the tabulated values themselves have an error (δ) no smaller than 10−15, fourth-order interpolation approaches this fundamental limit. A precise error analysis using context-specific c and λ values reveals that fifth-order interpolation achieves an error near 10−8, representing the practical optimum for this case.
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persistent - revert to persistent and finalize