Test input_output_response to given input
Iteration k = 0
[[2.]
 [0.]
 [0.]
 [0.]]
Iteration k = 1
[[ 2.01015452]
 [ 0.19538625]
 [-0.04868018]
 [-0.89463742]]
Iteration k = 2
[[ 2.02563117]
 [ 0.10849942]
 [-0.1       ]
 [-0.06098602]]
Iteration k = 3
[[ 2.04021802]
 [ 0.18261745]
 [-0.1       ]
 [ 0.06411258]]
Iteration k = 4
[[ 2.06461556]
 [ 0.30431167]
 [-0.1       ]
 [-0.0589616 ]]
Iteration k = 5
[[ 2.09882246]
 [ 0.37919961]
 [-0.1       ]
 [ 0.06212092]]
Iteration k = 6
[[ 2.14072416]
 [ 0.45942425]
 [-0.08985664]
 [ 0.12941114]]
Iteration k = 7
[[ 2.18955538]
 [ 0.51908751]
 [-0.07067371]
 [ 0.22892035]]
Iteration k = 8
[[ 2.24402253]
 [ 0.57296426]
 [-0.04527114]
 [ 0.24453612]]
Iteration k = 9
[[ 2.30304471]
 [ 0.61025855]
 [-0.02041629]
 [ 0.21806227]]
number of iterations: 10