HW3. Numerical Interpolation
1. Consider the function f(x,y) = 0.26(x2 + y2) − 0.48xy, where −1 ≤ x ≤ 1 and −1 ≤ y ≤ 1.
(1) Find and plot the Lagrange interpolating polynomial p(x,y) using equally spaced nodes with h = 0.2.
(2) Compare the computed result in Question 1-(1) with the exact function value.
2. Consider the function f(x,y) = sin(πx)sin(πy), where −1 ≤ x ≤ 1 and −1 ≤ y ≤ 1.
(1) Find and plot the Lagrange interpolating polynomial p(x,y) using equally spaced nodes with h = 0.2.
(2) Compare the computed result in Question 2-(1) with the exact function value.
(3) Do the same work with the Chebyshev nodes,
(4) Discuss why the Chebyshev nodes are generally better than equally spaced nodes in polynomial
n
interpolation. [Hint: Plot the functions Q |x − xi| for uniform and Chebyshev nodes.]
i=0
