[分析] 關於polynomials---數據分析的問題!
1a. Let I = {-1,-1/2,0,1/2,1}
and f(x) = 1/(1 + x^2). Find the value of each of the
following at x = 3=4.
i) The polynomial P(x) of degree 4 interpolating f(x) on the set I.
ii) The piecewise linear function L(x) defined on a mesh of width 1/2
interpolating f(x) on I.
iii) The piecewise quadratic function Q(x) defined on a mesh of width 1
interpolating f(x) on I.
1b. Using the error formula, find the smallest bound on the quantity
max x∈[-1;1]｜f(x)-L(x)｜ where L(x) is the approximation given in (ii).
As a computational check,f'''(x) = -24x(x^2- 1)/(1+x^2)^4
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