function []=hw5_2_1()

% Jacobi and Gauss-Seidel iterative methods
% set up A and b
A=diag(-4*ones(10,1))+diag(2*ones(9,1),-1)+diag(2*ones(9,1),1);
b=[2:11]';

% Jacobi
xold=zeros(10,1);
xnew=zeros(10,1);
tol=1;
iter=0;
while (tol>0.000005)
    for i=1:10
        % indeces to use in the ith eq of Jacobi
        ind=[[1:i-1],[i+1:10]];
        xnew(i)=(b(i)-A(i,ind)*xold(ind))/A(i,i);
    end
    tol=norm(xnew-xold);
    iter=iter+1;
    xold=xnew;
end
fprintf('Jacobi took %3.0d iterations and resulted in:\n',iter)
disp(xnew)

% Gauss-Seidel
xold=zeros(10,1);
xnew=zeros(10,1);
tol=1;
iter=0;
while (tol>0.000005)
    for i=1:10
        % indeces to use for x-values already computed - stored in xnew
        ind1=[1:i-1];
        % indeces to use for x-values from the previous iterate - stored in xold 
        ind2=[i+1:10];
        xnew(i)=(b(i)-A(i,ind1)*xnew(ind1)-A(i,ind2)*xold(ind2))/A(i,i);
    end
    tol=norm(xnew-xold);
    iter=iter+1;
    xold=xnew;
end
fprintf('Gauss-Seidel took %3.0d iterations and resulted in:\n',iter)
disp(xnew)