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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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受近期连续降水和上游水量增加的双重作用,我国第一大淡水湖鄱阳湖的水位连日攀升。截至4月6日上午8时,位于星子的标志性水文监测点记录到水位已达13.19米,较前一日增高0.28米,这是本年度水位首度超越13米大关。与此同时,湖口水文站测得水位12.91米,单日涨幅为0.29米。