.
. , . n , , . . n, , , , .
:
a11x1+a12x2+a13x3=b1
a21x1+a22x2+a23x3=b2 (1)
a31x1+a32x2+a33x3=b3
(1) : 1. 2, 3.
x2= (2)
x3=
.
x1(0)=0,x2(0)=0,x3(0)=0.
.
X1 =
X2(k+1) = (3)
X3(k+1) =
K=0,1,2,3, (3) -->C , X2(k)àC2, x3àc3, à , =(1,2,3) (2) , , (1). , .
. . (1) ,..
x1(k) x2(k) 3(k), (3) à (1) .
. (), :
max 1
. : x1(0)=x2(0)=x3(0)=0, :
X2(k+1)=
X3= .
32. . .
, , =f(). , . . / , . .
0 | 1 | n | ||
0 | 1 | n |
33. .
yi,i=0,n.
, i() n- .
, L i=0,n (3)
, i = 0.
I 0.
(4)
i(x) n 1 2 3 i()=(x-x0)(x-x(i-1))(x-x(i+1)).(x-xn) (5)
|
|
A i()=1=(x -x0)(x -x(i-1))(x -x(i+1)).(x -xn) (6)
:
0 | 1 | 2 | |
0 | 1 | 2 |
(-0)(-1)
,
) (x-x0)(x-x1)(x-x2)
.
N b0+b1(x-x0)+b2(x-x0)(x-x1)+_+bn(x-x0)(x-xn)
. bi .
i=0,n
Nn(x0)=b0
Nn(x1)=y0+b1(x1-x0)=y1, b1=(y1-y0)/(x1-x0)
y(x0,x1)= y(xi,xj)=
y(x0, x1,x2)=
b2=y(x0.x1.x2)
y(xi,xj,xk)= ..
.