Question

USING MATLAB

Create Inner-Product 3.2 The inner-product we will be using in the problem is defined as | p(x)q(x)dx (p(σ), g(α) And of course the corresponding norm, ||p(x)|| = /{p(x), q(x)) Implemnet each of these as functions as done in homework 12. (i.e. use polyint, polyval, conv to evaluate the integral of the polynomial. I would prefer that these are implemented in the same script as the rest of the project, but if they are in a seperate file, be sure to upload them as well.

Answer 1

MATLAB Script:

close all
clear
clc
format rat

syms x
f = [1 -2 0 0]; % x^3 - 2*x^2
g = [1 0]; % x
disp('Polynomials:')
fprintf('f = '), disp(f)
fprintf('g = '), disp(g)

r = inner_prod(f, g);
fprintf('\nInner Product of f and g ='), disp(r)
n = norm(f);
fprintf('Norm of f = '), disp(n)

% Inner Product
function r = inner_prod(p, q)
poly_prod = conv(p, q); % Multiplying p and q
poly_int = polyint(poly_prod); % Integrate p*q
r = (1/2) * (polyval(poly_int, 1) - polyval(poly_int, -1)); % Evaluate at the limits of integration, 1 and -1
end

% Norm
function n = norm(p)
n = sqrt(inner_prod(p, p));
end

Output:

Command Window Polynomials: f = 1/5 Inner Product of f and g = Norm of f = 2244/2311