[分析] 數據分析問題...求高手解答!
Let a = X0 < X1 <……. < XN = b, where xi = a + ih and h = (b - a)=N. Let
C(X) be a function satisfying:
(i) C(X) is a cubic polynomial Cj(x) on each subinterval [Xj-1; Xj ], j = 1,
….. ,N.
(ii) C(X) interpolates a given function f(x) at Xk/3, k = 0, 1, ….., 3N,
i.e., atX0, X1/3, X2/3,X1,…...
a) If |f^(4)．(X)| < = M4 for all X[a; b],
find an upper bound on |f(x) - C(x)| valid for all X[a; b] which depends
only on M4,and h (but does not depend on x).
b) If f(X) = 24e^3(x-1) and [a; b] = [0; 1], determine a value of h
that will guarantee an error of < = 10^-8 for all X[0; 1].
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