Алгоритм решения БДЗ / 03c

1

3x4 2x3 + 3x 1 = 0

0.9246; φ(x) = ((2x3 3x + 1)/3)(1=4), x0 = 1;

0.3467; φ(x) = 1/(3x3 2x2 + 3), x0 = 1; èëè φ(x) = ( 3x4 + 2x3 + 1)/3, x0 = 0; èëè φ(x) = 1/(3x3 2x2 + 3), x0 = 1;

2

x4 + 2x3 + 3x 1 = 0

2.5303; φ(x) = (1 3x 2x3)(1=4), x0 = 2;

0.3103; φ(x) = ( x4 2x3 + 1)/3, x0 = 1;

3

2x3 + 5x2 + 3x + 0.5 = 0

1.7071; φ(x) = ( 0.5 2x3 5x2)/3, x0 = 1.6; èëè φ(x) = 5/2 3/(2x) 1/(4x2), x0 = 1.6;

0.5000; φ(x) = ( 0.5 3x 2x3)/(5x), x0 = 0.4; èëè φ(x) = 3/5 2/5x2 1/(10x), x0 = 0.3;

0.2929; φ(x) = ( 0.5 2x3 5x2)/3, x0 = 0.1; èëè φ(x) = 1/6 2/3x3 5/3x2, x0 = 0.1;

4

x3 x2 + 3x 1 = 0

2.4142; φ(x) = 1/x2 + 3/x 1, x0 = 1;

1.0000;

0.4142; φ(x) = (x3 + x2 + 1)/3, x0 = 0.4; èëè φ(x) = (x2 + 1)/( x2 + 3), x0 = 0.25;

5

5x5 15x3 x2 + 3x 1 = 0

1.7183;

1.6115; φ(x) = 3/x + 1/(5x2) 3/(5x3) + 1/(5x4), x0 = 1.5;

0.6333;

6

5x3 x2 + 3x 0.5 = 0

0.9460;

0.5558;

0.1902; φ(x) = (5x3 + x2 + 0.5)/3, x0 = 0.1;

7

x3 x2 3x 1 = 0

2.4142; φ(x) = 1 + 3/x + 1/x2, x0 = 2.5;

1.0000; φ(x) = (3x + 1)/(x2 x), x0 = 1.2;

0.4142; φ(x) = 1/3(x3 x2 1), x0 = 0.5;

8

x3 x2 1 = 0

1.4656; φ(x) = (x2 + 1)(1=3), x0 = 1;

9

4x4 + x3 x2 1 = 0

0.8882; φ(x) = ((x2 + 1 x3)/4)(1=4), x0 = 1;

0.7312; φ(x) = ((x2 + 1 x3)/4)(1=4), x0 = 1;

10

x5 4x3 x2 1 = 0

2.1378; φ(x) = (4x3 + x2 + 1)(1=5), x0 = 2.5;

1.8109;

0.7797; φ(x) = x (x5 4x3 x2 1)/(5x4 12x2 2x), x0 = 1;

11

x3 x2 + 10x 1 = 0

3.7430; φ(x) = (x2 10x + 1)(1=3), x0 = 3;

2.6419; φ(x) = ( x2 + 10x 1)(1=3), x0 = 2;

0.1011; φ(x) = (x3 + x2 + 1)/10, x0 = 0;

12

5x3 5x2 + 0.5 = 0

0.8670;

0.4126;

0.2796;

13

x4 + 5x3 5x2 + 0.5 = 0

5.8519; φ(x) = ( 5x3 + 5x2 0.5)(1=4), x0 = 5;

0.6970; φ(x) = ( 5x3 + 5x2 0.5)(1=4), x0 = 0.6;

0.4361; φ(x) = ( 1/(2x2 + 10x 10))(1=2), x0 = 0.5;

0.2811; φ(x) = ( 1/(2x2 + 10x 10))(1=2), x0 = 1;

14

x4 + 5x3 5x2 + 2 = 0

5.8454; φ(x) = 5 + 5/x 2/x3, x0 = 3;

0.5221; φ(x) = x (x4 + 5x3 5x2 + 2)/(4x3 + 15x2 10x), x0 = 1;

15

x4 5x2 + 2 = 0

2.1358; φ(x) = (5x2 2)/x3, x0 = 2;

èëè φ(x) = 5/x 2/x3, x0 = 2;

2.1358; φ(x) = (5x2 2)(1=4), x0 = 2;

èëè φ(x) = 5/x 2/x3, x0 = 2;

0.6622; φ(x) = (x 2)/(1 + x3 5x), x0 = 0.5;

0.6622; φ(x) = ((x4 + 2)/5)(1=2), x0 = 1;

16

x4 + 5x3 x2 + 2 = 0

5.1787; φ(x) = x1 x13 5, x0 = 5.9;

0.7047; φ(x) = 3x4+10x3 x2 2 , x0 = 0.9;

4x3+15x2 2x

èëè φ(x) = (abs((x2 x4 2)/5)(1=3)), x0 = 1;

17

5x4 + x3 + x2 + 2x 2 = 0

0.9344;

√

0.5464; φ(x) = (2/(1 + x + 5x2 + 2/x)), x0 = 0.5;

18

9x3 + 3x2 + 6x + 1 = 0

1.0606; φ(x) = 1/3 + 2/(3x) + 1/(9x2), x0 = 1;

√

èëè φ(x) = ((6x + 1)/(9x 3)), x0 = 1;

0.5295; φ(x) = 1/3 + 2/(3x) + 1/(9x2), x0 = 1;

0.1979; φ(x) = 3/2x3 x2/2 1/6, x0 = 0; èëè φ(x) = (9x3 1)/(3x + 6), x0 = 0.1;

19

x3 + 3x2 6x + 1 = 0

4.4115; φ(x) = 3 + 6/x 1/x2, x0 = 5;

1.2267; φ(x) = ( 3x2 + 6x 1)(1=3), x0 = 5; èëè φ(x) = (( x3 + 6x 1)/3)(1=2), x0 = 1; èëè φ(x) = x2/3 + 2 1/(3x), x0 = 1.3;

0.1848; φ(x) = (x3 + 3x2 + 1)/6, x0 = 0.1;

20

4x3 6x + 1 = 0

1.3008; φ(x) = (abs((6x 1)/4))(1=3), x0 = 1;

1.1309; φ(x) = (6x 1)/(4x2), x0 = 1;

0.1699; φ(x) = (1 + 4x3)/6, x0 = 0;