Методичка по Информатике Ч_3

a11x1

a12 x2 ...

a1n xn

b1;

a21x1

a22 x2 ...

a2n xn

b2 ;

(25.1)

an1x1

an2 x2 ...

ann xn

bn

-

AX

B ,

A

a21

a22

...

a2n

b2

x2

.

...

....

....

an1

an2

...

ann

bn

xn

,

-

-

.

A

, . .

,

(25.1)

.

-

xi ,

i

1, 2, ..., n ,

-

.

-

(25.1)

1

b1

a12 x2

a13 x3

...

a11

1

a22

1

bn

an1x1

an2 x2

...

ann

b

n

a

x k

1

ij

x k

i

j

1

j

1

i

aii

i

i

1

x k

1

n

x k

1

b

a

ij

a

ij

x k

i

j

1

j

j

i 1

j

.

i

aii

X

0

x

0 , x

0

0

,

1

2

n

0

,

X

,

.

X

0

1

X .

1

2

X

, X ,

,

1 -

x k 1

i 1, 2, 3, ..., n ,

(25.3)

i

-

aij

1

(i

(25.4)

aii

j

aij

1

( j

(25.5)

aii

i

aii

n

aij

(i

(25.6)

j

i

j

1

-

.

0

0,25

.

0,25

1

0,5 ;

2

0,325 ;

3

0,85 .

,

max

i

0,85

.

-

,

0,25

0,75

1,

,

1.

i=1, n

x1i=(bi S)/aii+xi

ti=|x1i xi|

ti

35

,

x

0

, x

0

, x 0

,

, x 0 .

1

2

3

n

(25.2)

-

x

1

:

1

x

1

1

b

a

x

0

a

x

0

...

a

x

0 .

(25.7)

1

a11

1

12

2

13

3

1n

n

x 1

,

x

1

1

2

x 1

1

b

a

x 1

a

x 0 ...

a

x

0

.

.

(25.8)

23

2n

n

2

a22

2

21

1

3

x

1

x 1 ,

n

1

x 1

,

, x 1

:

2

n 1

x

1

1

b

a

n1

x

1

a

2

x

1

a

n3

x

1

...

a

n n 1

x 1

. (25.9)

n

n

2

ann

n

1

3

n 1

( x

1 ,

x

1 , ...,

1

2

xn1 ).

k -

x k

1

b

a

x k

1

a

x k

1

...

a

x k

1

;

1

a11

1

12

2

13

3

1n

n

x k

1

b

a

x k

a

23

x k

1

...

a

2n

x k

1

;

2

a22

2

21

1

3

n

(25.10)

x k

1

b

a

x k

a

x k

... a

x k

n

ann

n

n1

1

2

n 1

36

i

1

x k

n

x k

1

a

ij

a

ij

1

j

j

x k

j

j i

x k 1

(25.11)

i

aii

i

i

1

x k

n

b

a

ij

a

ij

x k

i

j

1

j

j i

1

.

(25.11a)

i

aii

,

-

, . .

x k