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Math Help - Interpolation

  1. #1
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    Interpolation

    How to determine an estimate for the maximum error committed in the interpolation process?

    For example:
    x |-35 | -1 | 1
    f(x) | -2 | -1 | 0

    Using Newton's method I found:
    p_2(x) = 0,5x^2+18,0294x+16,53

    Now what do I need to determine an estimate for the maximum error of interpolation?
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  2. #2
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    That depends upon what information you are given about the function f. If you have no information at all about f, then it is quite possible that f takes on values of, say 100000000000 for some x between -1 and 1, -100000000 for some other value of x between -1 and 1, and the error as large. On the other hand, if you know that f is a quadratic polynomial, then the formula you got is exact!
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    That depends upon what information you are given about the function f. If you have no information at all about f, then it is quite possible that f takes on values of, say 100000000000 for some x between -1 and 1, -100000000 for some other value of x between -1 and 1, and the error as large. On the other hand, if you know that f is a quadratic polynomial, then the formula you got is exact!
    There is a formula to determine the error in interpolation?
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  4. #4
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    Apparently you did not understand what I said: That depends on what information you are given about the function f.
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