function y = Arnoldi(A,v,t,tol,m)

n = size (v,1);
V = zeros(n  ,m+1);
H = zeros(m+1,m);

beta = norm(v);
V(:,1) = v/beta;
resnorm = inf;

j=0;

while resnorm > tol
    j = j+1;
    z = A*V(:,j);
    for i=1:j
        H(i,j) = z'*V(:,i);
        z  = z - H(i,j)*V(:,i);
    end
    H(j+1,j) = norm(z);
    e1 = zeros(j,1); e1(1) = 1;
    ej = zeros(j,1); ej(j) = 1;
    s  = [0.01, 1/3, 2/3, 1]*t;
    for q=1:length(s)
        u         = expm(-s(q)*H(1:j,1:j))*e1;
        beta_j(q) = -H(j+1,j)* (ej'*u);
    end
    resnorm = norm(beta_j,'inf');
    fprintf('j = %d, resnorm = %.2e\n',j,resnorm);
    if resnorm<=toler
       break
    elseif j==m
       disp('warning: no convergence within m steps');
    end
    V(:,j+1) = z/H(j+1,j);
end
y = V(:,1:j)*(beta*u);