Question

Problem 8. Define a function gs1_error(n) that accepts as input a non-negative integer n and outputs the error of the Gauss-Seidel approximation (xn, yn) to the solution of system (1). In other words, it should output the distance between the nth approximation (xn, yn) and the true value (x_val,y_val) of the solution to (1).

Answer 1

The MATLAB code will be:

close all;

clc;

clear all;

a = [20, 1, -2; 3, 20, -1; 2,-3, 20];

b = [17; -18; 25];

tol = 1e-6;

[M,N] = size(a);

if M~=N

error('A is not a square Matrix');

end

x = [0,0,0];

xx(1,:) = x;

n = 100;

error = 0.00001;

for k = 2:n

for i = 1:N

s = 0;

for j = 1:N

if j ~= i

s = s + a(i,j) * x(j);

end

end

x(i) = (1/a(i,i)*(b(i) - s));

end

xx(k,:) = x;kk = k;

Error = abs(max(xx(kk,:)- xx(k-1,:)))

if Error<error

break;

end

end

fprintf ('The roots of equation are: ')

x

fprintf ('The number of iterations are: ')

k

fprintf ('The error is: ')

Error

Step-by-step explanation: