Polynomial Interpolation

CharlesDarwin University

SMA104- Concepts of Mathematic

Project part B

Polynomial Interpolation

Note: Please submit your project part B solutions as a single .m file by 11:59 pm on 31

January 2021 in Learnline. Show all workings in detail, else you will lose marks.

An important problem in various science and engineering application is to find a polynomial

whose graph passes through a specified set of points in the plane; this is called an

interpolating polynomial for the points. Interpolating polynomial help scientist and engineers

to design solution to problems or understand the mechanisms of the systems they study. A

key skill for quantitative data analysis involves fitting models to data. A good model can be

used to predict the behaviour of the system in conditions not originally measured in

experiment.

In this project the lifting force on an aircraft wing measured in a wind tunnel at various wind

velocities is shown in the table below.

Velocity (100 ft/s) 1 2 4 8 16 32

Lifting force (100 lb) 0.00 3.12 15.86 33.70 81.50 123.00

Project Part B (Marks: 20)

a. Solve the augmented matrix from part A of the project to find the coefficients 𝑎0, 𝑎1,

…𝑎5. Model the data in the table above with your interpolating polynomial of degree

5. (Marks: 7)

b. Use the polynomial obtained in (a) to estimate the lifting force at 140 ft/s. (Marks: 3)

c. Show that the result from the interpolation is reasonable by graphing the polynomial

of degree 5 and the measured data in the same x-y coordinate. (Marks: 7)

d. Is the polynomial of degree 5 a good fit for the measured data? Are there any

distortions between the graph of the polynomial and the data? Explain (Type your

answer in the m.file). (Marks: 3)

Resources.

Note: Use the rref() function in MATLAB to perform Gauss-Jordan elimination and reduce

the augmented matrix to reduced row echelon form. From the reduced row echelon form,

extract the unknown coefficient 𝑎0, 𝑎1, 𝑎2…𝑎5 for the interpolating polynomial.

MATLAB access: Students can check that they have virtual access to MATLAB via these
links.

Link to the VMware Horizon client on the web page https://desktop.cdu.edu.au/.

Alternatively, VMware provides all the links to client for the different OS types below

(includes MacOS, Linux, Windows, iOS and Android versions):

https://my.vmware.com/en/web/vmware/info/slug/desktop_end_user_computing/vmware_hor

izon_clients/4_0

The server address is the same as the URL: https://desktop.cdu.edu.au

https://desktop.cdu.edu.au/

https://my.vmware.com/en/web/vmware/info/slug/desktop_end_user_computing/vmware_horizon_clients/4_0

https://my.vmware.com/en/web/vmware/info/slug/desktop_end_user_computing/vmware_horizon_clients/4_0

https://desktop.cdu.edu.au/