Re: linear interpolation error bound


In article <hQA3g.5431$Jk2.3402@fed1read03>,
"quat" <spam@xxxxxxxx> writes:

Is this homework?

None of this makes any sense unless you describe how the approximating
polynomial p(x) is obtained from the approximant function u(x).

Well I got my error estimation from lagrange polynomial theory of textbook.
So to anwer your question, p(x) is obtained by method of lagrange
polynomials.

N. Shamsundar
University of Houston



but you forgot something important:
you had
f(x) - p(x) = (1/2)*f''(xi_x)*(x-x(j))*(x-x(j+1))
where xi_x is some intermediate value between x(j) and x(j+1)
if x is in [x(j),x(j+1)].
you cannot directly differentiate this. but there are several
possibilities to correct this:
what is p' ?
now there is a rule in math for relating a secant slope with f'
proceed from this
hth
peter

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