I would like to you to complete the MATLAB Assignment in the attached document. Follow all the steps as outlined in the document. Annotate all code to see explain each line. Thank You. The Assignment is due thursday 21st february at 15.00 GMT. Document Preview: MA2895 Numerical analysis project, MATLAB Assignment, Spring Term 2013 Page 1 MA2895 MATLAB ASSIGNMENT I, Spring Term 2013 Deadline: 22th February 2013, 17:00 This assignment constitutes 35% of the assessment for the of MA2895 assessment block. It consists of two parts as described below. The ?rst part constitutes 20% of the assessment while the second part constitutes 15%. Please read part A of the assignment, including hints given on page 3, which is based on level 1 material, and start thinking about what you might need to do BEFORE you turn up for your scheduled labs. That way, you will be in a position to make the best use of the help available. Part A: Lagrange interpolation The aim here is to construct a Lagrange interpolant for a given function of a given order and test how well it performs as a function approximation. Brieøy, one way to construct a Lagrange interpolant is as follows. Suppose that we have n + 1 points xi, i = 0; 1; : : : ; n and a function g. We want to approximate this function by a polynomial using Lagrange interpolation. Given n+1 pairs of real numbers (xi; g(xi)); i = 0; : : : ; n with xi 6= xj ; i 6= j, let F(x) = Pni=0 fixi be the Lagrange interpolant, i.e. nth order polynomial which satis?es F(xi) = g(xi). This means that the following is true: f0 + f1x0 + f2x20+ + fnxn0= g(x0); f0 + f1x1 + f2x21+ + fnxn1= g(x1); f0 + f1xn + f2x2n + + fnxnn= g(xn); with the right hand side values g(xi) and the values xi, i = 0; 1; : : : ; n on the left hand side known. These are simply a set of linear equations in the coeñcients fi of the interpolating polynomial and can also be written as 26664 1 x0 x20 xn0 1 x1 x21 xn1 1 xn x2n xnn 37775 | {z } X 26664 f0 f1 fn37775 | {z } f = 26664 g(x0) g(x1) g(xn)37775 | {z } g : Hence the solution to the interpolation problem (i.e., the coeñcients of the interpolating polynomial) may be obtained by f = X­1g. You might want to look at the section on Attachments: MATLAB-Assign.pdf