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Math Help - Numerical Analysis Interpolation problem

  1. #1
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    Numerical Analysis Interpolation problem

    Find the function P(x) = a + b*cos(pi*x) + c*sin(pi*x), which interpolates the data:

    (0,2), (.5,5), (1,4)

    Can someone show what I need to do here please?

    The answer is: P(x) = 3 - cos(pix) + 2sin(pix)

    Thanks
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  2. #2
    MHF Contributor
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    Re: Numerical Analysis Interpolation problem

    Are you sure "interpolates" is the right word? Seems like "collocates" might be better.

    This could be a tricky problem, but you have been given wounderfully convenient values, 0, 1/2, and 1. Substitute away and you've three equations so solve simultaneously.

    P(x) = a + b*cos(pi*x) + c*sin(pi*x)

    P(0) = a + b*cos(pi*0) + c*sin(pi*0) = a + b = 2
    P(1/2) = a + b*cos(pi*(1/2)) + c*sin(pi*(1/2)) = a + c = 5
    P(1) = a + b*cos(pi*1) + c*sin(pi*1) = a - b = 4

    Are you letting the complicated appearance frighten you? Don't. Substitute and solve.
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