Mavzu: Algebraik va trancendent tenglamalarni yeshishda oraliqni teng ikkiga bo’lish, iteraciya usullari. Tayanch iboralar

5-laboratoriya ishi


Mavzu: Algebraik va trancendent tenglamalarni yeshishda oraliqni teng ikkiga bo’lish, iteraciya usullari. Tayanch iboralar: Tenglama, tenglamaning ildizlari, bir no‘malumli tenglamalar, algebraik tenglama, trancendent tenglama, tenglamalarni taqribiy yechish usullari, kesmani ikkiga bo’lish usuli. Algoritm blok-sxemasi Misol: Oraliqni teng ikkiga bo’lish usuli yordamida

Tenglamani biror ildizini 0.001 aniqlikda toping. Dastur matni (Paskalda)
Program Teng_bolish;
Label L1;
var
k:integer; a,b,c,eps:real;
function f(x:real):real;
begin
f:=sqrt(x+2)+0.7*x;
end;
begin k:=0;
L1:writeln(‘a,b=’); readln(a,b);
If f(a)*f(b)>0 then goto L1;
readln(eps);
while abs(b-a)>eps do
begin
C:=(a+b)/2; k:=k+1;
Writeln(k,c:6:5,f(c):8:5);
If f(a)*f(c)<0 then b:=c else
a:=c;
end;
End.
Laboratoriyalıq jumıstı orınlaw ushın tapsırmalar.
23-misol 24-misol

Javoblar
23-misol
#define _USE_MATH_DEFINES
#include
#include
using namespace std;
double func(double x)
{
return (3*x*x*x+2*x*x-15*x-14);
}
double find(double x0, double x1, double eps)
{ double left = x0, right = x1, x, fl, fr, f;
int iter = 0;
cout << "x0= " << x0 << " x1= " << x1 << " ";
do {
x = (left + right) / 2;
f = func(x);
if (f > 0) right = x;
else left = x;
iter++;
} while (fabs(f) > eps && iter<20000);
cout << iter << " iterations" << endl;
return x;
}
int main()
{ cout << find(0,3, 0.001);
cin.get(); return 0; }

24-misol
#define _USE_MATH_DEFINES
#include
#include
using namespace std;
double func(double x)
{
return (4*x*x*x-17*x*x-70*x-49);
}
double find(double x0, double x1, double eps)
{
double left = x0, right = x1, x, fl, fr, f;
int iter = 0;
cout << "x0= " << x0 << " x1= " << x1 << " ";
do {
x = (left + right) / 2;
f = func(x);
if (f > 0) right = x;
else left = x;
iter++;
} while (fabs(f) > eps && iter<20000);
cout << iter << " iterations" << endl;
return x;
}
int main()
{
cout << find(-3,0, 0.001);
cin.get(); return 0;
}