A DISCRETE DYNAMICAL SYSTEM AND ITS APPLICATIONS

ABSTRACT The main goal of this manuscript is to introduce a discrete dynamical system defined by symmetric matrices and a real parameter. By construction, we rediscovery the Power Iteration Method from the Projected Gradient Method. Convergence of the discrete dynamical system solution is established. Finally, we consider two applications, the first one consists in find a solution of non linear equation problem and the other one consists in verifies the optimality conditions when we solve quadratic optimization problems over linear equality constraints.

摘要 本研究的核心目标为介绍一种由对称矩阵与实参数定义的离散动力系统。基于构造过程，我们从投影梯度法（Projected Gradient Method）中重新推导出了幂迭代法（Power Iteration Method）。本文确立了该离散动力系统解的收敛性。最后，本文探讨了两类应用场景：其一用于求解非线性方程（nonlinear equation）问题的解，其二用于验证带线性等式约束的二次优化（quadratic optimization）问题求解时的最优性条件。