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.

Now graph the function and polynomial, and interpolation nodes.

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

Now graph the function and polynomial, and interpolation nodes.

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

Now graph the function and polynomial, and interpolation nodes.

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

Now graph the function and polynomial, and interpolation nodes.

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

Now graph the function and polynomial, and interpolation nodes.

(c) John H. Mathews 2004