在图像处理,机器学习和工程学等应用领域中,通常需要处理一些定义在Hilbert空间中的大规模算子方程。为求解这类算子方程及最值问题,构造了一类增量型不精确Broyden方法并证明了该算法的线性收敛和局部超线性收敛性。该算法降低了在处理大规模问题中所产生的储存成本,并通过应用证明了该算法的有效性。In application fields such as image processing, machine learning, and engineering, it is often necessary to solve large-scale operator equations defined in Hilbert spaces. To address such operator equations and optimization problems, a class of incremental inexact Broyden methods has been developed, and the linear convergence as well as local superlinear convergence of this algorithm has been proven. This algorithm reduces the storage costs associated with handling large-scale problems, and its effectiveness has been demonstrated through practical applications.
In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.
