MATLAB: How to fix the error (Index exceeds matrix dimensions)

error

could you please check my code. I got the following error 
Index exceeds matrix dimensionshow .
Error in NnNonSymmetricLanczos (line 17)
    r=A*V(:,j)-alpha*V(:,j)-gamma*V(:,j-1);
function [alpha,beta,gamma,T] = alg(A,v,n)
n=4;
 
c = ones(n,1);
t = ones(1,n)./(1:n);
A = toeplitz(c,t);
v = randn(n,1);
V=v; W=v/norm(v)^2;
beta=0; gamma=0;
alpha=W(:,1)'*A*V(:,1); T(1,1)=alpha;
for j=1:n
if j==1
    r=A*V(:,j)-alpha*V(:,j);
    p=A'*W(:,j)-alpha*W(:,j);
else
    r=A*V(:,j)-alpha*V(:,j)-gamma*V(:,j-1);
    p=A'*W(:,j)-alpha*W(:,j)-beta*W(:,j-1);
end
    beta=norm(r);
    gamma=r'*p/beta;
end
T(j+1,j)=beta;
T(j,j+1)=gamma;
V=[V,r/beta];
W=[W,p/gamma];
alpha=W(:,j+1)'*A*V(:,j+1);
T(j+1,j+1)=alpha;
end

Best Answer

V and W only have a single column, but you are indexing them V(:,j) and W(:,j) at j>1.
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