Solved-Computational methods and applications Homework 4 -solution

Description

Please submit to CANVAS a .zip  le that includes the following Matlab functions:

poly least squares.m

test least squares finance.m

test least squares interp.m

Exercise 1 Write a Matlab function poly least squares.m that implements the least squares method we discussed in class to approximate a data set in terms of a polynomial model of degree M. The function should be in the form

Output:

a: vector of coe  cients representing the polynomial (1)

err: Error between the model and the data in the 2-norm

Exercise 2 Use the function you coded in Exercise 1 to determine the least squares polyno-mial approximant of the attached nancial data set Dow Jones 2012 2017.dat (normalized closing price of the Dow Jones index from 2-14-2012 to 2-13-2017). To this end, write a Matlab function test least squares finance.m that plots in the same gure the data points fx_i; y_ig_i=1;:::;n (in blue) and the least-squares polynomial model (1) for M = 1; 2; 4; 8. Assume that the domain of the polynomial is the same as domain of the data points, i.e., plot the polynomial model in the interval [0; 1].

1

Exercise 3 Show that the least squares polynomial approximant can be an interpolant. To this end, apply the function you coded in Exercise 1 to the following data set

Set M=15 in (1), and write a Matlab function test least squares interp.m that returns a plot the data points (3) (blue circles) and a plot of the polynomial model (1) (red line) in the same gure.