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Recently, Yamashita and Fukushima [11] established an interesting quadratic convergence result for the Levenberg-Marquardt method without the nonsingularity assumption. This paper extends the result of Yamashita and Fukushima by using l k ¼ kF ðx k Þk d , where d 2 ½1; 2Š, instead of l k ¼ kF ðx k Þk 2 as the Levenberg-Marquardt parameter. If kF ðxÞk(More)
In this paper, we present a new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound(More)
We propose a new self-adaptive Levenberg-Marquardt algorithm for the system of nonlinear equations F(x) = 0. The Levenberg-Marquardt parameter is chosen as the product of F k δ with δ being a positive constant, and some function of the ratio between the actual reduction and predicted reduction of the merit function. Under the local error bound condition(More)
Before the developmental trajectory, outcomes, and related interventions of gratitude can be accurately and confidently studied among the youth, researchers must ensure that they have psychometrically sound measures of gratitude that are suitable for this population. Thus, considering that no known scales were specifically designed to measure gratitude in(More)