Abstract

For an overdetermined system of nonlinear equations, a two-stage method is suggested for constructing an error-stable approximate solution. The first stage consists in constructing a regularized set of approximate solutions for finding normal quasi-solutions of the original system. At the second stage, the regularized quasi-solutions are approximated using an iterative process based on square approximation of the Tikhonov functional and a prox-method. For this Newton-type method, a convergence theorem is proved and the Fejér property of the iterations is established. Additionally, the two-stage method is applied to the inverse problem of reconstructing heavy water (HDO) in the atmosphere from infrared spectra of solar light transmission.

中文翻译：

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非线性方程组的两阶段求解方法及其在大气反演中的应用

摘要

对于一个超定的非线性方程组，建议采用两步法构造误差稳定的近似解。第一阶段包括构造一组正规的近似解，以找到原始系统的标准拟解。在第二阶段，使用基于Tikhonov泛函和近似方法的平方近似的迭代过程来近似正则化准解。对于这种牛顿型方法，证明了一个收敛定理，并建立了迭代的费耶性质。此外，两步法还应用于从太阳光透射的红外光谱中重建大气中的重水（HDO）的反问题。