Example 1.   Form several Chebyshev polynomials of degree  n = 1,2, 3, 4, and 5  for the function    over the interval    using Chebyshev's nodes.

Solution 1.

1 (a).  Construct the Chebyshev interpolation polynomial  ,  of degree n = 1.

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Now graph the function and polynomial, and interpolation nodes.

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1 (b).  Construct the Chebyshev interpolation polynomial ,  of degree n = 2.

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Now graph the function and polynomial, and interpolation nodes.

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1 (c).  Construct the Chebyshev interpolation polynomial , of degree n = 3.

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Now graph the function and polynomial, and interpolation nodes.

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1 (d).  Construct the Chebyshev interpolation polynomial , of degree n = 4.

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Now graph the function and polynomial, and interpolation nodes.

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1 (e).  Construct the Chebyshev interpolation polynomial , of degree n = 5.

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Now graph the function and polynomial, and interpolation nodes.

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(c) John H. Mathews 2004