How Do You Solve a 7th Degree Polynomial Interpolation by Hand for Given Points?

[adamp1988]

Homework Statement

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).

Homework Equations

Don't know of any

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.

Thanks!

 

[dacruick]

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.

 

[Mark44]

A seventh-degree polynomial isn't linear...

 

[hotvette]

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.