Лабораторная работа № 2

Интерполирование и экстраполирование данных.

Интерполяционный многочлен Лагранжа.

Многочлен Лагранжа, принимающий заданные значения в узловых точках имеет вид:

[pic]

Задание . Восстановить многочлен Лагранжа, удовлетворяющий приведенным исходным данным.

Пример:

Варианты:

|1). | | | | |
|[pic] |0 |1 |2 |5 |
| | | | | |
|[pic] |2 |3 |12 |147 |
|2). | | | | |
|[pic] |-2 |1 |2 |4 |
| | | | | |
|[pic] |25 |-8 |-15 |-23 |
|3). | | | 0| | 2|
|[pic] |-2 |-1 | |1 | |
| | | | 2| | 6|
|[pic] |6 |0 | |0 | |
|4). | | | | |
|[pic] |0 |1 |2 |5 |
| | | | | |
|[pic] |3 |4 |13 |148 |
|5). | | | | |
|[pic] |-2 |1 |2 |4 |
| | | | | |
|[pic] |26 |-7 |-14 |-22 |
|6). | | | 0| | 2|
|[pic] |-2 |-1 | |1 | |
| | | | 1| | 5|
|[pic] |5 |0 | |0 | |
|7). | | | | |
|[pic] |-1 |0 |1 |4 |
| | | | | |
|[pic] |2 |3 |12 |147 |
|8). | | | | |
|[pic] |1 |2 |3 |6 |
| | | | | |
|[pic] |2 |3 |12 |147 |
|9). | | | | |
|[pic] |-3 |0 |1 |3 |
| | | | | |
|[pic] |25 |-8 |-15 |-23 |
|10). | | | | |
|[pic] |-1 |2 |3 |5 |
| | | | | |
|[pic] |25 |-8 |-15 |-23 |
|11). | | | -1| | 4|
|[pic] |-3 |-2 | |0 | |
| | | | 2| | 6|
|[pic] |6 |0 | |0 | |
|12). | | | 1| | 3|
|[pic] |-1 |0 | |2 | |
| | | | 2| | 6|
|[pic] |6 |0 | |0 | |
|13). | | | | |
|[pic] |2 |3 |4 |7 |
| | | | | |
|[pic] |2 |3 |12 |147 |
|14). | | | | |
|[pic] |-2 |-1 |0 |3 |
| | | | | |
|[pic] |2 |3 |12 |147 |
|15). | | | | |
|[pic] |-4 |-1 |0 |2 |
| | | | | |
|[pic] |25 |-8 |-15 |-23 |
|16). | | | | |
|[pic] |0 |3 |4 |6 |
| | | | | |
|[pic] |25 |-8 |-15 |-23 |
|17). | | | | |
|[pic] |-1 |0 |1 |4 |
| | | | | |
|[pic] |3 |4 |13 |148 |
|18). | | | | |
|[pic] |1 |2 |4 |6 |
| | | | | |
|[pic] |1 |2 |34 |146 |
|19). | | | | |
|[pic] |-3 |0 |1 |3 |
| | | | | |
|[pic] |26 |-7 |-14 |-22 |
|20). | | | | |
|[pic] |-1 |2 |3 |5 |
| | | | | |
|[pic] |26 |-7 |-14 |-22 |
|21). | | | -1| | 1|
|[pic] |-3 |-2 | |0 | |
| | | | 3| | 7|
|[pic] |7 |1 | |1 | |
|22). | | | 1| | 3|
|[pic] |-1 |0 | |2 | |
| | | | 1| | 5|
|[pic] |5 |-1 | |-1 | |
|23). | | | 1| | 3|
|[pic] |-1 |0 | |2 | |
| | | | 0| | 10|
|[pic] |2 |1 | |1 | |
|24). | | | | |
|[pic] |-2 |-1 |0 |1 |
| | | | | |
|[pic] |1 |6 |5 |4 |
|25). | | | | |
|[pic] |-3 |-2 |-1 |0 |
| | | | | |
|[pic] |40 |27 |12 |1 |
|26). | | | 0| | 2|
|[pic] |-2 |-1 | |1 | |
| | | | -1| | -7|
|[pic] |-27 |-4 | |-6 | |
|27). | | | | |
|[pic] |-1 |0 |1 |2 |
| | | | | |
|[pic] |-5 |-10 |-1 |34 |
|28). | | | 0| | 2|
|[pic] |-2 |-1 | |1 | |
| | | | 0| | 8|
|[pic] |16 |-1 | |1 | |
|29). | | | 0| | 2|
|[pic] |-2 |-1 | |1 | |
| | | | 1| | 9|
|[pic] |-23 |-6 | |-2 | |
|30). | | | | |
|[pic] |1 |2 |3 |4 |
| | | | | |
|[pic] |1 |2 |13 |40 |

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