求解非线性方程组的新的信赖域方法

The New Trust Region Method for Solving the System of Nonlinear Equations

通过将信赖域技巧与Levenberg-Marquardt算法有效结合到一起,进而提出新的信赖域方法,进而证明了新方法的全局收敛性,并且在局部误差界等条件下得到该算法的收敛阶为2δ2+δ,其中δ∈(1/2,1)并且给出了数值结果,在证明新方法的相关收敛性结果时,同时进行了数值实验,并验证了新的信赖域方法的可行性.

Through the combine of the new tru s t region technique and Levenberg-Marquardt algo-rithm together, it put forward a new trustregion method. It proved that the global convergence of the new method, and under the local error bound condition i t obtained the convergence order of the algo-rithm 2δ2＋δ and δ∈ （1/2,1） , and the numerical results are presented. I t not only proved the relevant convergence results of the new method , but also gave the numerical experiments, and verified the feasi-bility of the new trust region method.