Математика

     Министерство науки, высшей школы и технической политики Российской
                                 Федерации.

                        Новосибирский Государственный
                          Технический Университет.
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            Контрольная работа по специальным главам математики.


Факультет: АВТ.
Кафедра: АСУ.
Группа: А-513.
Студент: Борзов Андрей Николаевич.
Преподаватель: Хоменко Валентин Михайлович.
Дата: 10 мая 1997 года.



                             Новосибирск – 1997.
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Исходные данные.



|       |0      | 2     |4      |6      |8      |10     |12     |
|X1     |-10    |8.391  |-4.081 |-1.543 |6.669  |-9.65  |9.524  |
|X2     |3.536  |0.365  |-4.012 |4.881  |-2.368 |-1.785 |4.701  |
|X3     |0.721  |0.229  |0.721  |0.114  |6.835  |0.244  |0.252  |
|X4     |2.718  |1.94   |0.885  |0.439  |0.379  |0.631  |1.432  |
|X5     |0      |3.934  |-2.402 |-5.716 |-1.382 |-6.299 |-3.36  |
|X6     |0.667  |-0.099 |-0.465 |0      |0.635  |0.331  |-0.445 |
|X7     |8.999  |6.524  |1.183  |7.583  |1.021  |7.315  |1.011  |
|X8     |-7.568 |-0.484 |4.227  |-5.015 |-0.114 |6.974  |-2.05  |
|X9     |-0.661 |4.998  |-1.017 |1.683  |4.545  |-3.739 |3.496  |
| X10   |0      |-0.497 |-0.8   |0.247  |-0.008 |-0.397 |0.333  |
| X11   |1      |0.336  |0.931  |0      |0.143  |0.314  |0      |
| X12   |-4.741 |2.22   |0.01   |-4.854 |0.02   |0.006  |-4.55  |
| X13   |0      |-2.961 |-3.872 |-1.701 |-2.786 |-0.085 |-5.197 |
|X14    |0      |0.328  |1.339  |2.677  |4.247  |6.001  |7.907  |



1. Построим матрицу mxt(t).


|t      |0      |2      |4      |6      |8      |10     |12     |
|mxt    |-0.38  |1.8    |-0.525 |-0.086 |1.274  |-0.01  |0.932  |



2. Строим корреляционную матрицу.


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|       |0      |2      |4      |6      |8      |10     |12     |
|       |       |       |       |       |       |       |       |
|t      |       |       |       |       |       |       |       |
|0      |20.072 |-1.34  |0.655  |11.543 |-3.915 |7.718  |-1.858 |
|2      |-1.34  |9.03   |-1.198 |1.766  |4.212  |-5.479 |5.756  |
|4      |0.655  |-1.198 |5.341  |-0.267 |0.904  |8.101  |-1.556 |
|6      |11.543 |1.766  |-0.267 |12.725 |1.464  |6.552  |7.517  |
|8      |-3.915 |4.212  |0.904  |1.464  |8.862  |-2.406 |7.679  |
|10     |7.718  |-5.479 |8.101  |6.552  |-2.406 |20.64  |-3.602 |
|12     |-1.858 |5.756  |-1.556 |7.517  |7.679  |-3.602 |17.288 |


|t      |0      |2      |4      |6      |8      |10     |12     |
|Dx     |20.072 |9.03   |5.341  |12.725 |8.862  |20.64  |17.288 |
|(x     |4.48   |3.005  |2.311  |3.567  |2.977  |4.543  |4.158  |



3. Строим нормированную корреляционную матрицу.


|t      |0      |2      |4      |6      |8      |10     |12     |
|0      |1      |-0.1   |0.063  |0.722  |-0.294 |0.379  |-0.1   |
|2      |-0.1   |1      |-0.173 |0.165  |0.471  |-0.395 |0.461  |
|4      |0.063  |-0.173 |1      |-0.032 |0.131  |0.772  |-0.162 |
|6      |0.722  |0.165  |-0.032 |1      |0.138  |0.404  |0.507  |
|8      |-0.294 |0.471  |0.131  |0.138  |1      |-0.178 |0.62   |
|10     |0.379  |-0.395 |0.772  |0.404  |-0.178 |1      |-0.19  |
|12     |-0.1   |0.461  |-0.162 |0.507  |0.62   |-0.19  |1      |

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4. Строим таблицу ((t).


|t      |0      |2      |4      |6      |8      |10     |12     |
|(      |1      |-0.089 |0.277  |0.618  |-0.284 |0.42   |-0.1   |

      Строим график нормированной корреляционной функции (при  необходимости
аппроксимируем по методу наименьших квадратов).
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5. Найдем спектральную характеристику Sx(() и построим её график.

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