Question

In: Advanced Math

Find the Chebyshev interpolation nodes on the interval [4,12] for an interpolating polynomial of degree 5

Solutions

Expert Solution

The formula to calculate n Chebyshev nodes on an arbitrary interval [a,b] is given by

Since the interpolating polynomial is of degree 5 we will need 6 data points to find the unique polynomial of degree 5 that interpolates the data. The formula to calculate the six Chebyshev nodes required to find the degree 5 polynomial on the interval [4, 12] is given as

So we start with k = 1 and get

Next we have for k = 2, we get the Chebyshev node

Next for k = 3, the Chebyshev node can be calculated as

For k = 4, we have the fourth Chebyshev node to be calculated as

For k = 5, the fifth Chebyshve node can be calculated as

And lastly for k = 6, we get the final Chebyshev node as

Thus we have the six Chebyshev nodes to find an interpolating polynomial of degree 5 on the interval [4, 12] as

Colby Messinger answered 1 year ago

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