Результат
|
X1 |
X2 |
k |
|
1,000000 |
0,000000 |
0 |
|
-2,701922 |
-0,217900 |
1 |
|
-2,704933 |
-0,188844 |
2 |
|
-2,706982 |
-0,166831 |
3 |
|
-2,708403 |
-0,150145 |
4 |
|
-2,709405 |
-0,137491 |
5 |
|
-2,710121 |
-0,127891 |
6 |
|
-2,710639 |
-0,120606 |
7 |
|
-2,711010 |
-0,115077 |
8 |
|
-2,711297 |
-0,110879 |
9 |
|
-2,711504 |
-0,107693 |
10 |
|
-2,711659 |
-0,105273 |
11 |
|
-2,711775 |
-0,103436 |
12 |
|
-2,711862 |
-0,102041 |
13 |
|
-2,711927 |
-0,100982 |
14 |
|
-2,711977 |
-0,100177 |
15 |
|
-2,712014 |
-0,099566 |
16 |
|
-2,712042 |
-0,099102 |
17 |
|
-2,712064 |
-0,098750 |
18 |
|
-2,712080 |
-0,098482 |
19 |
|
-2,712092 |
-0,098279 |
20 |
|
-2,712102 |
-0,098124 |
21 |
|
-2,712109 |
-0,098007 |
22 |
|
-2,712114 |
-0,097918 |
23 |
|
-2,712110 |
-0,097850 |
24 |
|
-2,712121 |
-0,097799 |
25 |
|
-2,712124 |
-0,097760 |
26 |
|
-2,712126 |
-0,097730 |
27 |
|
-2,712127 |
-0,097708 |
28 |
|
-2,712128 |
-0,097691 |
29 |
|
-2,712129 |
-0,097678 |
30 |
Метод Ньютона-Рафсона с дроблением шага 1 модификация
Листинг программы
procedure TForm1.Button1Click(Sender: TObject);
const A=25;
B=0.9;
C=0.35;
D=0.35;
function F(x1,x2:double):double;
begin
F:=a*x1+b*x2 + exp(c*x1*x1+d*x2*x2);
end;
function F1(x1,x2:double):double;
begin
F1:=a + exp(c*x1*x1+d*x2*x2)*2*C*x1;
end;
function F2(x1,x2:double):double;
begin
F2:=B + exp(c*x1*x1+d*x2*x2)*2*D*x2;
end;
function FF11(x1,x2:double):double;
begin
FF11:=exp(c*x1*x1+d*x2*x2)*2*C*x1*2*C*x1+exp(c*x1*x1+d*x2*x2)*2*C;
end;
function FF12(x1,x2:double):double;
begin
FF12:=exp(c*x1*x1+d*x2*x2)*2*C*x1*2*D*x2;
end;
function FF22(x1,x2:double):double;
begin
FF22:=exp(c*x1*x1+d*x2*x2)*2*D*x2*2*D*x2+exp(c*x1*x1+d*x2*x2)*2*D;
end;
label metka;
var k,N0,N1,N2,N:integer;
x:array [1..2, 0..300] of double;
matr:array[1..2,1..2] of double;
matr1:array[1..2] of double;
P1,P2,dd,E2,det,x1,x2,y,L,delta,fP:double;
begin
x[1,0]:=1; x[2,0]:=0; E2:=0.0004;
delta:=0.05;
matr1[1]:=F1(x[1,0],x[2,0]);
matr1[2]:=F2(x[1,0],x[2,0]);
k:=0; L:=1; N0:=0; N1:=2; N2:=0;
matr[1,1]:=FF11(x[1,k],x[2,k]);
matr[1,2]:=FF12(x[1,k],x[2,k]);
matr[2,1]:=matr[1,2];
matr[2,2]:=FF22(x[1,k],x[2,k]);
N2:=N2+3;
repeat
det:=matr[1,1]*matr[2,2]+matr[2,1]*matr[1,2];
P1:=(matr[1,2]*matr1[2]+matr[2,2]*matr1[1])/det;
P2:=(matr[1,1]*matr1[2]+matr[2,1]*matr1[1])/det;
y:=F(x[1,k],x[2,k]);
N0:=N0+1;
fP:=matr1[1]*P1+matr1[2]*P2;
metka:
if (F(x[1,k]-L*P1, x[2,k]-L*P2)-y)>(-delta*L*fP) then
begin
L:=L/2;
N0:=N0+1;
goto metka;
end;
x[1,k+1]:=x[1,k]-L*P1;
x[2,k+1]:=x[2,k]-L*P2;
matr1[1]:=F1(x[1,k+1],x[2,k+1]);
matr1[2]:=F2(x[1,k+1],x[2,k+1]);
N1:=N1+2;
dd:=SQRT(matr1[1]*matr1[1]+matr1[2]*matr1[2]);
k:=k+1;
until (dd<=E2);
x1:=x[1,k];
x2:=x[2,k];
y:=F(x1,x2);
N:=N0+N1+N2;
Label11.Caption:='x1='+FloatToSTr(x1)+' x2='+FloatToSTr(x2)
+' y='+FloatToSTr(y);
Label8.Caption:='N=N0+N1+N2='+IntToSTR(N0)+'+'+IntToSTR(N1)+
'+'+IntToSTR(N2)+'='+IntToSTR(N)+' k='+IntToStr(k);
end;