Abstarct: In this thesis, we describe a problem of best approximation. The best approximation is solving linear equation systems. Linear equation systems are three types. Determined, Underdetermined, Overdetermined system. Underdetermined equation system have infinite answer. We are looking for answers to the lowest norm. Answer it obtains by a neural network converges. Overdetermined equation system usually do not have any answer and we are looking for the approximation solution. In this case, the approximation solution converges approached by a neural network model. Answer determined system usually is unique and do not need to approximated. According to theorem, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution point to the optimal solution of the strictly convex quadratic optimization problem.