New fourth and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis

[EN] In this paper, a two-step class of fourth-order iterative methods for solving systems of nonlinear equations is presented. We further extend the two-step class to establish a new sixth-order family which requires only one additional functional evaluation. The convergence analysis of the proposed classes is provided under several mild conditions. A complete dynamical analysis is made, by using real multidimensional discrete dynamics, in order to select the most stable elements of both families of fourth- and sixth-order of convergence. To get this aim, a novel tool based on the existence of critical points has been used, the parameter line. The analytical discussion of the work is upheld by performing numerical experiments on some application-oriented problems. We provide an implementation of the proposed scheme on nonlinear optimization problem and zero-residual nonlinear least-squares problems taken from the constrained and unconstrained testing environment test set. Finally, based on numerical results, it has been concluded that our methods are comparable with the existing ones of similar nature in terms of order, efficiency, and computational time and also that the stability results provide the most efficient member of each class of iterative schemes.This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE), Generalitat Valenciana PROMETEO/2016/089Kansal, M.; Cordero Barbero, A.; Bhalla, S.; Torregrosa Sánchez, JR. (2021). New fourth and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis. Numerical Algorithms. 87(3):1017-1060. https://doi.org/10.1007/s11075-020-00997-4S1017106087

The oculomotor salience of flicker, apparent motion and continuous motion in saccade trajectories

The aim of the present study was to investigate the impact of dynamic distractors on the time-course of oculomotor selection using saccade trajectory deviations. Participants were instructed to make a speeded eye movement (pro-saccade) to a target presented above or below the fixation point while an irrelevant distractor was presented. Four types of distractors were varied within participants: (1) static, (2) flicker, (3) rotating apparent motion and (4) continuous motion. The eccentricity of the distractor was varied between participants. The results showed that saccadic trajectories curved towards distractors presented near the vertical midline; no reliable deviation was found for distractors presented further away from the vertical midline. Differences between the flickering and rotating distractor were found when distractor eccentricity was small and these specific effects developed over time such that there was a clear differentiation between saccadic deviation based on apparent motion for long-latency saccades, but not short-latency saccades. The present results suggest that the influence on performance of apparent motion stimuli is relatively delayed and acts in a more sustained manner compared to the influence of salient static, flickering and continuous moving stimuli.</p

Can Winter-Active Bumblebees Survive the Cold? Assessing the Cold Tolerance of Bombus terrestris audax and the Effects of Pollen Feeding

There is now considerable evidence that climate change is disrupting the phenology of key pollinator species. The recently reported UK winter activity of the bumblebee Bombus terrestris brings a novel set of thermal challenges to bumblebee workers that would typically only be exposed to summer conditions. Here we assess the ability of workers to survive acute and chronic cold stress (via lower lethal temperatures and lower lethal times at 0°C), the capacity for rapid cold hardening (RCH) and the influence of diet (pollen versus nectar consumption) on supercooling points (SCP). Comparisons are made with chronic cold stress indices and SCPs in queen bumblebees. Results showed worker bees were able to survive acute temperatures likely to be experienced in a mild winter, with queens significantly more tolerant to chronic cold temperature stress. The first evidence of RCH in any Hymenoptera is shown. In addition, dietary manipulation indicated the consumption of pollen significantly increased SCP temperature. These results are discussed in the light of winter active bumblebees and climate change

Best practices for comparing optimization algorithms

Comparing, or benchmarking, of optimization algorithms is a complicated task that involves many subtle considerations to yield a fair and unbiased evaluation. In this paper, we systematically review the benchmarking process of optimization algorithms, and discuss the challenges of fair comparison. We provide suggestions for each step of the comparison process and highlight the pitfalls to avoid when evaluating the performance of optimization algorithms. We also discuss various methods of reporting the benchmarking results. Finally, some suggestions for future research are presented to improve the current benchmarking process.Comment: Optim Eng (2017