In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.
[1] To investigate the morphology and distribution of pressure ridges in the northwestern Weddell Sea, ice surface elevation profiles were measured by a helicopter-borne laser altimeter during Winter Weddell Outflow Study with the German R/V Polarstern in 2006. An optimal cutoff height of 0.62 m, derived from the best fits between the measured and theoretical ridge height and spacing distributions, was first used to separate pressure ridges from other sea ice surface undulations. It was found that the measured ridge height distribution was well modeled by a negative exponential function, and the ridge spacing distribution by a lognormal function. Next, based on the ridging intensity R i (the ratio of mean ridge sail height to mean spacing), all profiles were clustered into three regimes by an improved k-means clustering algorithm: R i ≤ 0.01, 0.01 < R i ≤ 0.026, and R i > 0.026 (denoted as C 1 , C 2 , and C 3 respectively). Mean (and standard deviation) of sail height was 0.99 (AE0.07) m in Regime C 1 , 1.12 (AE0.06) m in C 2 , and 1.17 (AE0.04) m in C 3 , respectively, while the mean spacings (and standard deviations) were 232 (AE240) m, 54 (AE20) m, and 31 (AE5.6) m. These three ice regimes coincided closely with distinct sea ice regions identified in a satellite radar image, where C 1 corresponded to the broken ice in the marginal ice zone and level ice formed in the Larsen Polynya, C 2 corresponded to the deformed first-and second-year ice formed by dynamic action in the center of the study region, and C 3 corresponded to heavily deformed ice in the outflowing branch of the Weddell Gyre. The results of our analysis showed that the relationship between the mean ridge height and frequency was well modeled by a logarithmic function with a correlation coefficient of 0.8, although such correlation was weaker when considering each regime individually. The measured ridge height and frequency were both greater than those reported by others for the Ross Sea. Compared with reported values for other parts of the Antarctic, the present ridge heights were greater, but the ridge frequencies and ridging intensities were smaller than the most extreme of them. Meanwhile, average thickness of ridged ice in our study region was significantly larger than that of the Coastal Ross Sea showing the importance of deformation and ice age for ice conditions in the northwestern Weddell Sea.
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