.02832 1 = 2.45, two = 1.85 0.04985 0.0158 0.04707 0.0154 0.05245 0.0193 0.06001 0.02202 0.08574 0.03117 1 = 1.85, two = 1.65 0.05563 0.01850 0.05443 0.01899 0.05044 0.01751 0.05259 0.01889 0.05855 0.Mathematics 2021, 9, 2737 13 of13 ofathematics 2021, 1,3.four. Examples on the Linearization Process three.4. Examples of In
.02832 1 = two.45, two = 1.85 0.04985 0.0158 0.04707 0.0154 0.05245 0.0193 0.06001 0.02202 0.08574 0.03117 1 = 1.85, 2 = 1.65 0.05563 0.01850 0.05443 0.01899 0.05044 0.01751 0.05259 0.01889 0.05855 0.Mathematics 2021, 9, 2737 13 of13 ofathematics 2021, 1,three.4. Examples of your Linearization Procedure 3.four. Examples of In this subsection, the usage of the proposed Scaffold Library Formulation algorithm is demonstrated on the testing the Linearization Procedure functions introduced on the proposed algorithm is examples are primarily based ontesting In this subsection, the use in Section three.2. The following demonstrated around the calculations with random parameters 3.two. The in Section 3.three. functions introduced in Section selected following examples are primarily based on calculations with random parameters chosen in Section three.three. Example 3. Let a function f 1 , whose graph could be noticed in Figure 2, be provided. The chosen parameters Example three.are a= 0.69, 1 , = two.45, two = 1.65, and also the metricbe 1 is employed. In this parameters = 3, eight, 12, Let function f 1 whose graph can be Diversity Library MedChemExpress observed in Figure two, d given. The chosen instance, D = 180, and I 2 100. This function has twois utilised. In components, so the choice3, 8, 12,linear parts are = 0.69, = two.45, = = 1.65, plus the metric d1 monotone this example, = on the will depend on This function has we monotone parts, Figure three, we can see the distinction D = 80, and I = 100.the accuracy of whattwo would like to obtain. Inso the option from the linear components in between is dependent upon 3, eight,accuracypoints. we would like to get. In Figure three, we can see the distinction amongst the and 12 of what three, eight, and 12 points.Figure 2. The graphs from the functions f 1functions ,fandf (two)., f (three) , f (4) , and f (five) . Figure two. The graphs of the , f two , f three , f 4 (1) , f1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.two 0.2 0.2 0.four 0.6 0.2 0.8 0.four 1.0 0.6 0.eight 0.two 1.0 0.two 0.2 0.four 0.six 0.2 0.eight 0.four 1.0 0.6 0.8 0.2 1.0 0.4 0.four 0.two 0.2 0.four 0.6 0.two 0.8 0.4 1.0 0.six 0.8 1.0 0.6 0.6 0.four 0.four 0.8 0.eight 0.six 0.6 1.0 1.0 0.eight 0.8 1.0 1.Figure three. The graphs on the original function f 1 (the black line) and its piecewise linearizations l f1 Figure three. The graphs of the original function f 1 (the black line) and its piecewise linearizations l f1 (the red line), where = three, 8, 12. (the red line), exactly where = 3, eight, 12.Instance 4. Let a function f 2 , whose graph is depicted in Figure 2, be provided. The initial parameters Instance four. Let a function f two , whose graph is depicted in Figure two, be offered. The initial parameters are = 0.69, 1 = 2.45, two = 1.65; the metric d1 is chosen; = 12, I = one hundred. As we can see, are = 0.69, 1 = two.45, two = 1.65; the metric d1 is selected; = 12, I = one hundred. As we can see, the very first monotone parts are narrower, so if we pick out D = 80, the algorithm can not approximate the very first monotone parts are narrower, so if we pick out D = 80, the algorithm can not approximate the initial part appropriately. For illustration, we take D = 500 and D = 1000 (see Figure four). the very first component appropriately. For illustration, we take D = 500 and D = 1000 (see Figure 4).Mathematics 2021, 9,14 of1.1.1.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.1.0.0.0.0.1.0.0.0.0.1.Figure 4. The graphs with the original function f 2 (the black lines) and its piecewise linearizations l f2 (the red lines), exactly where D = 80, 500, 1000.Example five. Let a function f 5 be provided, and its graph is often noticed in Figure 2. The initial parameters = 0.69, 1 = two.45, 2 = 1.65 together with the metric d1 were chosen. In the very first a part of Figure five, = 12, 40, 100, I = 100, and D = 80. Within the second a part of the figure, = 25, 60, one hundred, I = 100, and D.
