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A Family of Least Change Diagonally Quasi-Newton Methods for Nonlinear Equations

机译：一个最不改变对角线准牛顿的非线性方程方法的家庭

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摘要

A new family of least-change weak-secant methods for solving systems of nonlinear algebraic equations is introduced. This class of methods belongs to that of quasi-Newton family, except for which the approximation to the Jacobian, at each step, is updated by means of a diagonal matrix. The approach underlying such approximation is based upon the commonly used least change updating strategy with the added restriction that full matrices are replaced by diagonal matrices. Using some appropriate matrix norms, some members of this family are introduced. Convergence results are proved, and particular members of the family that seem to be of practical usefulness are also considered.
机译：介绍了一种用于解决非线性代数方程系统的最小变化弱割线方法。这类方法属于Quasi-Newton系列的方法，除了在每个步骤中对雅可比的近似值，通过对角线矩阵更新。这种近似的基础方法基于通常使用的最小变化更新策略，其中具有对对角线矩阵替换的附加限制。使用一些适当的矩阵规范，介绍了一些这个家庭成员。还考虑了融合结果，并且还考虑了似乎实际有用的家庭成员。

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