  This paper deals with the error processing problem of sparse identification
of nonlinear dynamical systems(SINDy) through introducing the $L_\infty$
approximation to take place of the former $L_2$ approximation. The motivation
is that the $L_\infty$ approximation could better describe the error phenomenon
in the SINDy, which consists of the derivative approximation error and the
measurement noise. Then, an iterative thresholding algorithm is proposed to
solve the reformulated problem. 3 scenarios of possible errors are considered
in the experiment. The results show that the $L_\infty$ approximation performs
better or at least equal than the $L_2$ approximation in face of different
error cases. Hence, it is reasonable to consider the $L_\infty$ approximation
in the applications of the SINDy.
