Численные методы _методичка

№15

ì7.5x1 +1.8x2 - 2.1x3 -7.7x4 =1.1

ì1.2x1 +1.8x2 - 2.7x3 - 7.5x4 = 1.3

ï-10x +1.3x -20x -1.4x =1.5

№30ïï10x

+5.3x -2.7x

-5.4x

=2.2

ï

1

2

3

4

í

í

1

2

3

4

+6.9x3 +14.8x4 =10

ï2.8x1-1.7x2+3.9x3+4.8x4 =1.2

ï8.8x1-9.7x2

ï

+ 31.4x2

-2.1x3

-10x4 = -1.1

ï

+ 3.4x2

- 3x3 - 2.2x4

= 34.1

î10x1

î10x1

Лабораторная работа № 6

№1

ì2.4x1

- 0.3x2

+ 0.1x3

= 9.5

№16

ì- 2.1x1 - 3.5x2 + 0.1x3 = 1.5

ï

+1.6x2

+ 9.2x3

= 8.6

ï

+1.1x2 + 3.5x3 = 8.7

í4.3x1

í5.8x1

ï0.4x

-1.9x

+ 0.5x

= 3.1

ï

- 0.9x2 - 4.83 = -1.8

2

3

î0.2x1

î

1

ì1.1x1

- 4.3x2

+ 1.1x3

= 7.5

№17

ì1.8x1 - 4.7x2 +1.1x3 = 9.5

№2

ï5.8x

+ 1.8x

+ 2.5x

= 2.7

ï

+ 0.8x

+ 2.1x

= 5.7

2

3

í5.9x

2

3

í

1

ï

1

ï

+ 0.2x2

- 4.8x3

=1.5

+ 0.7x2 - 5.8x3 = 2.6

î0.2x1

î1.2x1

ì2.1x1

- 3.3x2

+ 0.1x3

= 5.5

ì2.1x1 - 6.3x2 + 0.1x3 = 5.8

№3

ï4.3x

+ 1.3x

2

+ 9.1x

3

= 8.3

№18

ï2.3x +1.8x

+ 9.1x

= 4.3

í

1

í

1

2

3

ï

- 1.9x2 + 0.5x3 = 4.3

ï

-1.5x2

+ 0.5x3 = 4.8

î3.4x1

î3.4x1

ì2.1x1

- 3.3x2

+ 0.1x3

= 5.5

ì3.1x1 - 6.1x2 + 0.9x3 = 6.5

№4

ï5.8x

+ 1.2x

2

+ 3.5x

3

= 7.7

№19

ï5.8x +1.6x

+ 2.5x

= 9.7

í

1

í

1

2

3

ï

+ 0.9x2

- 4.8x3

= 1.3

ï

+ 2.9x2

- 6.8x3 = 1.8

î0.2x1

î0.2x1

ì2.3x1 - 3.2x2 + 0.1x3 = 4.5

ì2.1x1 - 4.2x2 + 0.7x3 = 4.6

№5

ï0.3x

+ 1.3x

2

+ 5.2x

3

= 5.5

№20

íï0.8x + 3.3x

+ 5.6x

= 5.8

í

1

ï

1

2

3

ï

-1.9x2

+ 0.5x3

= 3.2

-1.6x2

+ 0.9x3 = 3.8

î3.4x1

î5.4x1

ì1.1x1

- 3.3x2

+ 0.1x3

= 5.5

ì1.7x1 - 3.9x2 + 0.1x3 = 5.1

№6

ï5.2x

+1.1x

2

+ 3.5x

3

= 7.7

№21

íï5.2x1 +1.2x2 + 3.5x3 = 7.2

í

1

ï

ï2.2x

+ 0.9x

- 4.9x

=1.8

- 4.8x3 = 1.3

2

3

î2.2x1 + 0.4x2

î

1

ì0.1x

- 0.9x

2

+ 3.4x

3

= 8.5

ì0.4x1 - 0.7x2 + 3.4x3

= 2.5

1

№22

ï

№7

ï4.3x

+ 1.3x

+ 2.2x

= 6.4

+1.4x2

+ 2.6x3

= 3.4

2

3

í5.3x1

í

1

ï

ï

- 8.9x2 + 1.5x3 = 3.3

- 8.9x2

+ 2.5x3

= 3.5

î2.8x1

î2.8x1

21

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ì0.1x1 - 2.2x2

+ 4.4x3

= 3.2

ì0.1x1 - 2.2x2 + 5.4x3 = 3.6

№8

ï3.3x

+ 1.8x

2

+ 0.2x

3

= 4.8

№23

íï3.3x1 +1.6x2 + 0.1x3 = 4.5

í

1

ï

ï3.4x - 7.1x

+ 0.5x

= 2.5

- 8.1x2

+ 0.5x3 = 2.2

2

3

î3.4x1

î

1

ì2.1x1 - 3.3x2

+ 0.1x3

= 5.9

ì2.1x1 - 5.3x2 + 0.1x3 = 5.8

№9

ï7.8x

+ 2.1x

2

+ 3.5x

3

=1.2

№24

íï9.1x1 + 2.1x2 + 2.5x3 = 1.2

í

1

ï

ï0.1x

+ 3.6x

- 2.8x

= 5.8

+ 3.6x2

- 6.7x3 = 5.7

1

2

3

î0.6x1

î

ì3.1x1 - 3.3x2

+ 0.1x3

= 2.5

ì3.5x1 - 3.3x2 + 0.1x3 = 3.5

№10

ï5.8x

+ 0.1x

2

+ 3.5x

3

= 6.8

№25

íï6.8x + 0.3x

2

+ 3.5x

= 6.3

í

1

ï

1

3

ï3.1x

+ 0.9x

- 4.8x

= 2.5

+ 0.8x2

- 4.8x3 = 2.5

2

3

î2.1x1

î

1

ì1.1x1 - 4.3x2

+ 2.1x3

= 3.5

ì1.6x1 - 4.3x2 +1.1x3 = 3.4

№11

ï4.3x

+ 2.3x

2

+ 6.2x

3

= 8.5

№26

íï3.3x + 2.4x

2

+ 7.2x

= 8.5

í

1

ï

1

3

ï3.4x -1.9x

+ 0.7x

= 9.3

-1.8x2 + 0.5x3 = 9.1

2

3

î3.4x1

î

1

№12

ì9.1x1 - 3.3x2

+ 0.1x3

= 5.5

№27

ì6.1x1 - 3.5x2 + 0.1x3 = 5.8

ï- 8.8x + 7.1x

+ 3.5x

= 9.7

ï

+ 0.5x

= 9.3

2

3

í- 5.8x + 7.1x

í

1

ï

1

2

3

ï0.2x

+ 0.9x

- 4.8x

=11.8

2

3

î0.2x1 + 0.7x2 - 4.8x3 = 1.5

î

1

№13

ì2.1x1 - 3.3x2

+ 0.1x3

= 5.1

№28

ì8.1x1 - 3.5x2 + 0.6x3 = 5.3

ï

4.3x

+ 1.3x

+ 9.2x

= 8.2

ï

+ 0.5x

= 9.7

í

2

3

í- 6.1x + 7.1x

2

1

ï

1

3

ï3.4x -1.9x

+ 0.5x

= -7.3

2

3

î0.2x1 + 0.9x2 - 4.8x3 =11.8

î

1

№14

ì12.1x1 - 3.3x2 + 0.1x3

= 8.5

ì6.1x1 + 3.1x2 + 0.6x3 = 5.5

ï

+ 1.1x

+ 3.5x

= 7.7

№29

ï

+ 3.5x

= 9.7

í0.8x

1

2

3

- 8.8x + 7.1x

2

3

ï

í

1

+ 9.9x2

- 4.8x3 = -1.8

ï0.7x + 0.5x

- 4.8x

= 1.8

î0.2x1

î

1

2

3

№15

ì2.1x1 - 3.3x2

+ 0.1x3

= 5.5

ì3.1x1 - 3.3x2 + 0.1x3 = 6.5

ï

+ 1.3x2

+ 9.2x3

= 18.5

№30

ï6.3x +1.3x

+ 9.2x

=1.5

í4.3x1

ï

í

1

2

3

-1.9x2

+ 0.5x3

= 3.3

ï5.4x -1.8x

+ 0.9x

= 3.7

î3.4x1

î

1

2

3

22

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Лабораторная работа № 7

x	y	№вар	x
0,48	1,52597	1	0,563
0,52	1,77734	7	0,518
0,57	1,89986	13	0,684
0,66	2,03045	19	0,752
0,71	2,22867	25	0,648
0,77	2,97373
x	y	№вар	x
0,22	2,56781	3	0,376
0,45	2,15630	9	0,473
0,49	1,87347	15	0,582
0,58	1,73456	21	0,602
0,61	1,49658	27	0,636
0,71	1,27895
x	y	№вар	x
0,66	0,70866	5	0,854
0,74	0,87252	11	0,809
0,82	1,01997	17	0,774
0,89	1,22578	23	0,975
0,91	1,37896	29	0,711
0,98	1,49876

x	y	№вар	x
0,03	1,08923	2	0,155
0,11	1,10956	8	0,044
0,16	1,17565	14	0,175
0,18	1,24896	20	0,248
0,27	1,37834	26	0,345
0,38	1,97566
x	y	№вар	x
0,39	2,78918	4	0,627
0,44	2,25613	10	0,424
0,53	2,078925	16	0,668
0,64	1,76203	22	0,517
0,67	1,65726	28	0,773
0,78	1,523478
x	y	№вар	x
0,09	8,04789	6	0,114
0,18	6,78969	12	0,235
0,24	4,58972	18	0,352
0,32	3,48932	24	0,285
0,37	2,69456	30	0,436
0,48	2,35789

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Содержание:
Лабораторная работа № 1 Метод бисекции..............................		3
Лабораторная работа № 2 Метод хорд......................................		5
Лабораторная работа № 3 Метод Ньютона...............................		5
Лабораторная работа № 4	Метод простых итераций ...............	6
Лабораторная работа № 5	Метод Гаусса ..................................	7
Лабораторная работа № 6	Метод простых итераций .............	12
Лабораторная работа № 7	Метод Лагранжа ...........................	15
Варианты заданий к лабораторным работам..........................		17

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