中文摘要：

<正>1引言考虑非线性方程组问题:F(x)=0,x∈R~n(1)其中,F:R~n→R~n为连续可微的非线性映射.我们讨论大规模情形,并假设F(x)的Jacobian矩阵无法获取,或存储量太大无法承受.仅在极其特殊的情况下,求解非线性方程组(1)才可能有直接解法,对大部分问题要依赖迭代法.已有的迭代方法有多种[1],常用方法大多是基于Newton法的,这些方法理论上有很多好的性质,如它们具有局部超线性收敛性,但在实际计算过程中,很多方法在

英文摘要：

Hierarchical-multivariate spectral gradient algorithm is proposed in this paper for large-scale nonlinear systems. The search direction is determined by a diagonal matrix and the nonlinear mapping according to the structure of Jacobian matrix. The layers are reduced along with the increase in the number of iterations and the decrease in the difference of diagonal elements in the diagonal matrix. In order to avoid calculating the Jacobian matrix and solving linear equations, the line search in each iteration step is taken in a systematic way. At the same time the non-monotone line search guarantcs the global convergence of the algorithm. Numerical experimental results show good.