2.2. Интерполяционные сплайны
Тема: Построение интерполяционного кубического сплайна.
Задание: В соответствии с вариантом задания (номер варианта задания соответствует номеру студента в группе) построить интерполяционный кубический сплайн для функции , заданной таблицей, и найти его значение в указанной точке x. Для решения системы алгебраических уравнений применить метод прогонки.
Варианты индивидуальных заданий
Группа №1
№ п/п |
|
0.24 |
0.26 |
0.27 |
0.29 |
0.30 |
0.32 |
0.37 |
0.38 |
0.42 |
0.49 |
0.59 |
|
1 |
|
0.2449 |
0.3004 |
0.3452 |
0.3714 |
0.4053 |
0.4382 |
0.4777 |
0.5080 |
0.5649 |
0.5784 |
0.6107 |
0.53 |
2 |
|
0.2553 |
0.3203 |
0.3764 |
0.4111 |
0.4586 |
0.5080 |
0.5726 |
0.6269 |
0.7445 |
0.7761 |
0.8595 |
0.54 |
3 |
|
1.2711 |
1.297 |
1.310 |
1.336 |
1.350 |
1.377 |
1.448 |
1.462 |
1.522 |
1.632 |
1.804 |
0.34 |
4 |
|
0.2355 |
0.2544 |
0.2637 |
0.2823 |
0.2915 |
0.3097 |
0.3544 |
0.3631 |
0.3976 |
0.4556 |
0.5330 |
0.33 |
5 |
|
0.7788 |
0.7334 |
0.6977 |
0.6771 |
0.6505 |
0.6250 |
0.5945 |
0.5712 |
0.5273 |
0.5169 |
0.4916 |
0.41 |
6 |
|
1.2840 |
1.3630 |
1.4330 |
1.4770 |
1.5370 |
1.6000 |
1.6820 |
1.7510 |
1.8960 |
1.9350 |
2.0340 |
0.43 |
7 |
|
0.1823 |
0.2624 |
0.3365 |
0.4700 |
0.5306 |
0.6419 |
0.7419 |
0.7885 |
0.8755 |
0.9555 |
0.9933 |
0.35 |
8 |
|
1.0630 |
1.0910 |
1.1190 |
1.1700 |
1.1930 |
1.2390 |
1.2810 |
1.3010 |
1.3390 |
1.3750 |
1.3920 |
0.39 |
9 |
|
0.3012 |
0.2725 |
0.2466 |
0.2019 |
0.1827 |
0.1496 |
0.1225 |
0.1108 |
0.0907 |
0.0743 |
0.0672 |
0.25 |
10 |
|
1.4920 |
1.9350 |
2.2930 |
3.5610 |
3.9350 |
4.0550 |
4.6650 |
5.5290 |
7.5380 |
12.1820 |
16.2810 |
0.56 |
11 |
|
0.6703 |
0.5169 |
0.4350 |
0.2800 |
0.2541 |
0.2466 |
0.2144 |
0.1809 |
0.1327 |
0.0821 |
0.0614 |
0.58 |
12 |
|
0.2474 |
0.3051 |
0.3523 |
0.3802 |
0.4169 |
0.4529 |
0.4969 |
0.5312 |
0.5972 |
0.6131 |
0.6518 |
0.40 |
13 |
|
0.2526 |
0.3150 |
0.3678 |
0.4000 |
0.4434 |
0.4875 |
0.5438 |
0.5897 |
0.6846 |
0.7090 |
0.7712 |
0.45 |
14 |
|
1.031 |
1.048 |
1.066 |
1.077 |
1.094 |
1.112 |
1.138 |
1.161 |
1.212 |
1.226 |
1.263 |
0.50 |
15 |
|
1.029 |
1.034 |
1.037 |
1.042 |
1.045 |
1.052 |
1.069 |
1.073 |
1.090 |
1.122 |
1.179 |
0.44 |
16 |
|
0.7866 |
0.7711 |
0.7634 |
0.7483 |
0.7408 |
0.7261 |
0.6907 |
0.6839 |
0.6570 |
0.6126 |
0.5543 |
0.48 |
17 |
|
0.2423 |
0.2629 |
0.2733 |
0.2941 |
0.3045 |
0.3255 |
0.3785 |
0.3892 |
0.4325 |
0.5098 |
0.6248 |
0.51 |
18 |
|
0.2447 |
0.2660 |
0.2768 |
0.2984 |
0.3093 |
0.3314 |
0.3879 |
0.3994 |
0.4466 |
0.5334 |
0.6696 |
0.28 |
19 |
|
0.2374 |
0.2571 |
0.2667 |
0.2860 |
0.2955 |
0.3146 |
0.3616 |
0.3709 |
0.4078 |
0.4706 |
0.5564 |
0.52 |
20 |
|
0.0792 |
0.1139 |
0.1461 |
0.2041 |
0.2304 |
0.2788 |
0.3222 |
0.3424 |
0.3802 |
0.4150 |
0.4314 |
0.36 |
Группа №2
№ п/п |
|
1.2 |
1.3 |
1.4 |
1.6 |
1.7 |
1.9 |
2.1 |
2.2 |
2.4 |
2.6 |
2.7 |
|
1 |
|
0.0792 |
0.1139 |
0.1461 |
0.2041 |
0.2304 |
0.2788 |
0.3222 |
0.3424 |
0.3802 |
0.4150 |
0.4314 |
1.68 |
2 |
|
0.1823 |
0.2624 |
0.3365 |
0.4700 |
0.5306 |
0.6419 |
0.7419 |
0.7885 |
0.8755 |
0.9555 |
0.9933 |
1.37 |
3 |
|
1.0630 |
1.0910 |
1.1190 |
1.1700 |
1.1930 |
1.2390 |
1.2810 |
1.3010 |
1.3390 |
1.3750 |
1.3920 |
1.62 |
4 |
|
0.3012 |
0.2725 |
0.2466 |
0.2019 |
0.1827 |
0.1496 |
0.1225 |
0.1108 |
0.0907 |
0.0743 |
0.0672 |
2.46 |
5 |
|
1.4920 |
1.9350 |
2.2930 |
3.5610 |
3.9350 |
4.0550 |
4.6650 |
5.5290 |
7.5380 |
12.1820 |
16.2810 |
2.64 |
6 |
|
0.6703 |
0.5169 |
0.4350 |
0.2800 |
0.2541 |
0.2466 |
0.2144 |
0.1809 |
0.1327 |
0.0821 |
0.0614 |
1.39 |
7 |
|
0.2553 |
0.3203 |
0.3764 |
0.4111 |
0.4586 |
0.5080 |
0.5726 |
0.6269 |
0.7445 |
0.7761 |
0.8595 |
2.35 |
8 |
|
1.2711 |
1.297 |
1.310 |
1.336 |
1.350 |
1.377 |
1.448 |
1.462 |
1.522 |
1.632 |
1.804 |
2.53 |
9 |
|
0.2355 |
0.2544 |
0.2637 |
0.2823 |
0.2915 |
0.3097 |
0.3544 |
0.3631 |
0.3976 |
0.4556 |
0.5330 |
1.56 |
10 |
|
1.029 |
1.034 |
1.037 |
1.042 |
1.045 |
1.052 |
1.069 |
1.073 |
1.090 |
1.122 |
1.179 |
2.38 |
11 |
|
0.7866 |
0.7711 |
0.7634 |
0.7483 |
0.7408 |
0.7261 |
0.6907 |
0.6839 |
0.6570 |
0.6126 |
0.5543 |
2.48 |
12 |
|
0.2423 |
0.2629 |
0.2733 |
0.2941 |
0.3045 |
0.3255 |
0.3785 |
0.3892 |
0.4325 |
0.5098 |
0.6248 |
2.51 |
13 |
|
0.2447 |
0.2660 |
0.2768 |
0.2984 |
0.3093 |
0.3314 |
0.3879 |
0.3994 |
0.4466 |
0.5334 |
0.6696 |
2.50 |
14 |
|
0.2374 |
0.2571 |
0.2667 |
0.2860 |
0.2955 |
0.3146 |
0.3616 |
0.3709 |
0.4078 |
0.4706 |
0.5564 |
1.55 |
15 |
|
0.7788 |
0.7334 |
0.6977 |
0.6771 |
0.6505 |
0.6250 |
0.5945 |
0.5712 |
0.5273 |
0.5169 |
0.4916 |
2.31 |
16 |
|
1.2840 |
1.3630 |
1.4330 |
1.4770 |
1.5370 |
1.6000 |
1.6820 |
1.7510 |
1.8960 |
1.9350 |
2.0340 |
2.02 |
17 |
|
0.2474 |
0.3051 |
0.3523 |
0.3802 |
0.4169 |
0.4529 |
0.4969 |
0.5312 |
0.5972 |
0.6131 |
0.6518 |
1.82 |
18 |
|
0.2526 |
0.3150 |
0.3678 |
0.4000 |
0.4434 |
0.4875 |
0.5438 |
0.5897 |
0.6846 |
0.7090 |
0.7712 |
2.05 |
19 |
|
1.031 |
1.048 |
1.066 |
1.077 |
1.094 |
1.112 |
1.138 |
1.161 |
1.212 |
1.226 |
1.263 |
1.61 |
20 |
|
0.2449 |
0.3004 |
0.3452 |
0.3714 |
0.4053 |
0.4382 |
0.4777 |
0.5080 |
0.5649 |
0.5784 |
0.6107 |
1.43 |