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Homework Help: Linear Algebra Question

  1. Mar 23, 2010 #1
    1. The problem statement, all variables and given/known data
    Given the following points, generate the function of the curve in form of a 7th degree polynomial.
    (1.301, -0.788)
    (1.477, -0.454)
    (1.602, -0.194)
    (1.700, 0)
    (1.778, 0.158)
    (1.845, 0.288)
    (1.903, 0.410)
    (1.954, 0.500)

    Furthermore, the solution has to be done without a calculator (during exams).

    2. Relevant equations
    Don't know of any

    3. The attempt at a solution
    I tried using the interpolation polynomial, however the graph equation has to be an exact match because I am required to calculate numerous addition details from the equation.

  2. jcsd
  3. Mar 23, 2010 #2
    haha that function doesn't sound very linear to me. I have no idea how to do that, but i would try using the method of least squares.
  4. Mar 23, 2010 #3


    Staff: Mentor

    A seventh-degree polynomial isn't linear...
  5. Mar 23, 2010 #4


    User Avatar
    Homework Helper

    The question seems a bit odd considering the points are given with three digit accuracy, a 7th degree polynomial is involved, and you are asked to solve it w/o a calculator.

    Since this appears to be from a linear algebra class and you have 8 data points to represent a 7th degree polynomial (with 8 unknowns), the problem can be represented in matrix form Ax = b where A is a 8 x 8 matrix, x is the unknown vector of the polynomial coefficients, and it can solved with techniques learned in linear algebra (e.g. Gauss elimination). But, the solution by hand, even algebraically, would be a real bear, much less tying to do the computations with points to 3 digit accuracy.

    I think you need clarification as to what is being asked and how it relates to linear algebra.
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