This is a two-member group project. While discussion with other students is encouraged, all work submitted for credit, however, must be your own. Any evidence of plagiarism or other forms of scholastic dishonesty will be grounds for a failing grade in the course. Newtons divided-difference interpolating polynomial The general formula for an nth-order polynomial is given as !() = " + # + $$ + + !! An alternative form that is well-suited for computer implementation is known as the Newtons divided-difference polynomial !() = " + #( ") + $$( ")( #) + + !( ")( #) ( !%#) (1) where b0, b1, b2, ..., bn can be evaluated from data points using the following equations: " = (") # = [#, "] $ = [$, #, ",] : (2) : ! = /!, !%#, , #, " 1 The bracketed functions in equation (3) are known as finite divided differences. For example, the first finite divided difference is represented generally as /', (1 = (') 2(3 ' ( (3) 2 The second finite divided difference, which represents the difference of two first divided differences, is expressed generally as /', (, )1 = /' (1 /( )1 ' ) (4) Similarly, the nth finite divided difference is [!, !%#, , #, "] = /!, !%#, , #1 [!%#, !%$, , "] ! " (5) Using these formulas and pseudocode shown in Figure 1 write an Octave1 script that determine the parameters b0, b1, b2, ..., bn where n depends on the number of data points used. For this project, n can be any number between 3 and 9. Use data points given in Figure 2 to determine the parameters b0, b1, b2, ..., bn and approximate the values of ln(3), ln(5) and ln(3.256) with error analysis for every approximation.