摘要
设f(x)、f’(x)及f”(x)在节点x_j(j=0,1,…,n)上的扰动界分别为ε、ε’及ε”,我们将给出两类分段三次Hermite插值的局部稳定界,并用它们讨论三次样条函数的局部稳定界。当节点上的导数代之以差商时。
Let ε, ε' and ε' be, respectively, perturbation bounds for f(x), f' (x) and f'(x) at knots x_j (j=0, 1, …, n). We will give local stability bounds for twotypes of piecewise Cubje Hermite interpolations and for cubic spline functions.When derivatives at knots replaced by divided differences, Corresponding resultscan be simplified.
关键词
三次H插值
样条函数
稳定界
均差
perturbation bounds
local stability bounds
piecewise cubich ermite interpolation
cubic spline function
divided difference
