bisection

>>> x= np.matrix([[2,3],[4,5],[5,6],[6,7]]).T
>>> x
matrix([[2, 4, 5, 6],
        [3, 5, 6, 7]])
>>> u,s,vh = np.linalg.svd(x)
>>> u
matrix([[-0.63626513, -0.77147047],
        [-0.77147047,  0.63626513]])
>>> s
array([ 14.13594166,   0.41851331])
>>> vh
matrix([[-0.25374621, -0.45291732, -0.55250288, -0.65208843],
        [ 0.87417635,  0.22805428, -0.09500675, -0.41806779],
        [-0.41253131,  0.79111926,  0.06788672, -0.44647467],
        [ 0.03530567,  0.3420343 , -0.82529127,  0.4479513 ]])

>>> u.T[0] * x
matrix([[-3.58694167, -6.40241286, -7.81014846, -9.21788406]])
>>> vh[0] * s[0]
matrix([[-3.58694167, -6.40241286, -7.81014846, -9.21788406]])

>>> u.T[1] * x
matrix([[ 0.36585444,  0.09544375, -0.03976159, -0.17496693]])
>>> vh[1] * s[1]
matrix([[ 0.36585444,  0.09544375, -0.03976159, -0.17496693]])

>>> (u.T[0] * x - vh[0] * s[0]).sum()
6.2172489379008766e-15
>>> (u.T[1] * x - vh[1] * s[1]).sum()
7.4107386893729199e-15