MTH3051 Introduction to Computational Mathematics Assignment 2 ...

SCHOOL OF MATHEMATICAL SCIENCESMTH3051Introduction to Computational MathematicsAssignment 2. Root finding.Due date: Lab class for week 5This assignment contains just one question worth 35 marks (equal to 6% of the finalmark for this unit).Late submissions will be subject to late penalties (see the unit guide for fulldetails).1. Root findingThe functionf(x) = x − tan xhas a root at x = 0. Your game is to find the next 4 positive roots.(a) Use Matlab to plot the function f(x) and hence, by visual inspection, estimate thefirst four roots (within ±0.5 would be sufficient). 5/35(b) Use a suitable fixed point method to estimate the first 4 positive roots. 10/35(c) Using the Newton-Raphson method, estimate the first 4 positive roots. 10/35(d) Use your results to show that for the fixed point method ɛ n+1 = O (ɛ n ) while forNewton-Raphson, ɛ n+1 = O (ɛ 2 n) where ɛ n = |x n − x| is the error in the currentestimate of the root. 10/352. What to hand inWhen submitting the assignment you should include✦ Complete answers to the questions,✦ A clear statement of the equations you used and how you derived them,✦ Printouts of your Matlab programs, results and plots (if any).

School of Mathematical SciencesMonash UniversityMarks will be awarded for correctness as well as elegance (in particular how well youdocument the working of your Matlab programs. It should be easy for any body toread and understand your program. So use well chosen comments, but not so detailedthat it becomes hard to find the code!). But, and this is important, do not rely onthe comments in your Matlab code as the primary place in which you describe youralgorithm. There should be a separate discussion of the algorithm including any newequations you derived. This discussion should clearly describe your algorithm.Marks will be lost for poorly written programs, lack of clear and meaningfulcomments, and for an inadequate discussion.16-Feb-2014 2