关于线性插值及二次插值余项定理适用区间的分析

AN ANALYSIS OF THE SUITABLE RANGE OF THE THEOREM FOR LINEAR AND TWICE INTERPOLATIONS

本文针对线性插值及二次擂值余项估计中［ａ，ｂ］区间的某些不确定性，在证明误差限的过程中，定量分析了与余项定理中误差限估计条件相容的［ａ，ｂ］区间的限制条件，并给出了确切表达式，从而能避免对于［ａ．ｂ］认识上的模糊性和取法上的盲目性，进一步明确了余项估计的适用范围。

In relation to some indefiniteness of the range (a,b) in the remainder estimation for linear and twice interpolations, the author quantitatively analyses tile limited conditions of the mange (a, b), which are in conformity to the estimated conditions of the error limitation in the remainder theorem,andthus advances a clear-cut formula and avoids the ambiguity in comprehension and blindness in selection, with the result of further ascertaining theapplicable scope of remainder estimation.