CS3911 Reading List: Week 11

• Polynomial interpolation and approximation slides are in Inter-Approx.pdf.
• Section 9.1
• Solutions to Exam 2
• Section 11.1 to Section 11.3 (read ahead)

• Study the fit command of gnuplot, and use it to do the following approximation problems: Problems P9.31, P9.38, P9.50 Note that you have to choose a degree of the approximation polynomial properly. Plotting the data points and reviewing the shape of the approximation polynomial would help.

• Given four data points in the xy-plane: X₀ = (1,1), X₁ = (2,3), X₂ = (3,3) and X₃ = (4,4), find an approximation polynomial of degree 1. Use a calculator and the least square method discussed in class to solve this problem. (Answer: y = 0.5 + 0.9x)
• Given the following 5 points in the xy-plane: X₀ = (-2,0), X₁ = (-1,2), X₂ = (0,1), X₃ = (1,2) and X₄ = (2,0), find the interpolating polynomial of degree 4, P₄(x), with the divided difference method.
• Evaluate P₄(x) at x = 0.5, x = -0.5, x = -1.5 and x = 1.7 with the nested form.
• Now, add a new point X₅ = (3,-4) and find the new interpolating polynomial of degree 5, P₅(x). Note that you should not start from scratch.

You do not have to turn in your paper. What I really expect you to do is using these problems to gauge your understanding of the subject. So, do the problems after finish reading the above sections.