Math 6010, Fall 2016, Project on Orthogonal Polynomials

(Due: Monday December 12, 2016)

1- Introduction:

Set up a fourth-order polynomial regression model, using the Forsythe-Hayes algorithm, though you are not asked to solve the model.

2- Your Project:

Consider the data \( x_i := \frac{i}{100}, \) for $i=1,\ldots,100$. Find polynomials, \(\varphi_0,\ldots,\varphi_4\) such that: The report-writing portion of this project is straight-forward. Just write out what you did carefully, attach a copy of your program, and display careful formulas for the 5 polynomials. The coefficients of these polynomials should be stated explicitly in numerical terms.