# Traffic Data Interpolation

## Summary

The goal of this assignment is for students to demonstrate understanding of numerical interpolation through an intensive writing prompt. Two methods are implemented in MATLAB, Lagrange interpolation, and Neville's method. Students will critique the .m files and interpret the results in the context of traffic density data interpolation.

## Learning Goals

Students will reinforce their understanding of numerical interpolation and their implementation of Neville's method in the context of traffic data density.

Student's goal is to summarize the results obtained using two methods provided, each attempting to produce the Lagrange interpolating polynomial evaluated at time T=1.55 in technical writing style.

## Context for Use

This assignment is offered as homework in conjunction with skills-practice homework from classical numerical analysis modules on numerical interpolation. Students in this course are typically math and/or computer science majors in their junior or senior year of undergraduate studies. Providing an appendix is optional and only necessary if students do not have the access to run the program themselves.

## Description and Teaching Materials

In this assignment students are asked to analyze the interpolation results used to obtain an estimate of traffic conditions within a two hour time span along Highway 101 in California. For simplicity, we are considering traffic conditions at a given location and time is represented discretely by the nodes T_i for i=1,... 21, and evenly spaced between the interval from [1,3]. The corresponding values collected in a vector Y correspond to values measuring traffic density and are stored in the file found on our OCMS in uTrafficData.xlsx. The values can range from -1 to 1. Values closer to 1 indicate less traffic. Values closer to -1 indicate heavy traffic.

Student's goal is to summarize the results obtained using two methods provided, each attempting to produce the Lagrange interpolating polynomial evaluated at time T=1.55 in technical writing style. Compare the two methods and identify traits that make the method more or less desirable than the other. What do the results indicate about traffic conditions at this specific time? Which method do you recommend? Which result do you anticipate is the most accurate and why? Which implementation is the best and why? (2 page max)
Main Description and Prompt (Acrobat (PDF) 209kB Aug17 18)

## Teaching Notes and Tips

Teaching can follow the Burden and Faires text on Numerical Analysis, sections on "Interpolation," including Neville's Method.

## Assessment

Mathematics Writing Rubric (Acrobat (PDF) 71kB Oct10 18) is used to grade assignment. The aim is for students to demonstrate their understanding of interpolation (pros and cons), the benefits of different methods, and to do so in writing.