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Math Help - Lagrange

  1. #1
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    Lagrange

    Using the Lagrange method to find the polynomial that interpolates the points:

    f(x) | -3 | -2 | -1 | 0 | 1 |
    x | -197 | -35 | -1 | 1 | 5 |

    I find:
    p(x) = y_0 L_0(x) + y_1 L_1(x) + y_2 L_2(x) + y_3 L_3(x) + y_4 L_4(x)

    L_0(x) = \frac{x^4 + 30x^3 - 176x^2 -30x -175}{1269952992}

    L_1(x) = \frac{x^4 + 192x^3 -986x^2 -192x + 985}{-7931520}

    L_2(x) = \frac{x^4 +228x^3 -402x^2 -4750x + 4925}{779968}

    L_3(x) = \frac{x^4 +228x^3 + 52x^2 -5100x -4925}{-57024}

    L_4(x) = \frac{x^4 +232x^3 +984x^2 -232x -985}{193920}

    So I got the following polynomial:
    p(x) = 4.124x10^{-4}x^4 + 9,55x10^{-4}x^3 +5,34x10^{-3}x^2 +4,845x10^{-3}x + 0,0111

    Is this correct what I did?
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  2. #2
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    I would say no, because your

    p(-197)=614036\not=-3.

    Can you show all your intermediate steps?
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  3. #3
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    Are you sure you don't have "x" and "f(x)" reversed?
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    Are you sure you don't have "x" and "f(x)" reversed?
    The problem statement is the same. But I'm also thinking that it is upside down
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  5. #5
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    Using Newton's interpolation I find:

    p_4(x) = 3.216x10^{-6}x^4 +8.11522x10^{-4}x^3 + 0,0375x^2 +0,4991x -0,53807

    It seems more reasonable. But the method of Lagrange I could not.
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  6. #6
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    You need to show your work. If you don't do that, we can't help you very much. Here's a page on the Lagrange Interpolating Polynomial.
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  7. #7
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    Quote Originally Posted by Ackbeet View Post
    You need to show your work. If you don't do that, we can't help you very much. Here's a page on the Lagrange Interpolating Polynomial.
    Thanks. I managed to solve the problem.
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  8. #8
    A Plied Mathematician
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    Ok, have a good one.
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