Question

Write your own MATLAB code to solve the system

10 − x + sin(x + y) − 1 = 0

8y − cos2 (z − y) − 1 = 0

12z + sin(z) − 1 = 0

using a residual tolerance of 10^−6 and the initial guess, ~x 0 = [0.1, 0.25, 0.08]^T . Print out the values for x, y and z for each iteration in a table similar to the one you created for the problems of the previous homework. You should submit your code (which can again be organized as a function and the script calling this function) together with your output.

Answer 1

clc

clear all

close all

format long

ff=@(x,y,z) [10-x+sin(x+y)-1;8*y-cos(z-y)^2-1;12*z+sin(z)-1];

f=@(x) ff(x(1),x(2),x(3));

g=@(x,y,z) [cos(x + y) - 1, cos(x + y), 0;0, 2*cos(y - z)*sin(y - z) + 8, -2*cos(y - z)*sin(y - z);0, 0, cos(z) + 12];

J=@(x) g(x(1),x(2),x(3));

x0=[0.1;0.25;0.08];

for i=1:100

x1=x0-inv(J(x0))*f(x0);

fprintf('Iteration %d, x=%f, y=%f, z=%f\n',i,x1);

if(norm(x1-x0)<1e-6)

break;

end

x0=x1;

end