function [gamma, x] = inviter(A, s, numiter)
% INVITER   Shifted inverse iteration for the closest eigenvalue
%
% Input:
%   A         square matrix
%   s         value close to targeted eigenvalue (complex scalar)
%   numiter   number of iterations
%
% Output: 
%   gamma     sequence of eigenvalue approximations (vector)
%   x         final eigenvector approximation
%
    n = length(A);
    x = randn(n, 1);
    x = x/norm(x, inf);
    gamma = zeros(numiter, 1);
    B = A - s*eye(n);
    [L, U] = lu(B);
    for k = 1:numiter
        y = U\(L\x);
        [~, m] = max(abs(y));
        gamma(k) = x(m)/y(m) + s;
        x = y/y(m);
    end 
end