Dasturiy injinering” fakulteti 312-20 guruh talabasi Amirqulov Amirqulning

f(x)=x²-x-1; f'(x)=2x-1; f"(x)=2; hosilarga x₀=2,5 nuqtani kuyamiz; f(2,5)=2,75; f"(2,5)=2 kiymatlardan f(2,5)f"(2,5)>0 shart bajarilishini ko’rish kiyin emas, demak x₀=b=2,5 нуктани boshlangich yechim qilib olamiz.

[-1;0] oralikda esa x₀=-1 nuqtani boshlangich yechim qilib olish mumkin, chunki bu nuqtada ham f(x₀)f"(x₀)>0 shart bajariladi (tekshirib ko’rish o’quvchilarga xavola).
Berilgan tenglamani ildizini urimalar usuli bilan taqribiy yechish algoritmining blok–sxemasini va paskal dasturlashtirish tilida dasturini tuzish uchun quyidagi belgilashlarni kiritamiz.


f(x)=fx; f'(x)=f1x; у= f(x)/f'(x)=fx/f1x; x₀=x0; =eps.
Tenglamaning ildizini urinmalar usulida taqribiy hisoblash algoritmining blok–sxemasini va paskal tilidagi dasturini tuzamiz.


Program Nyuton(input,output);

Uses crt;

label 2

var x0, x, y, fx, f1x, eps :real;

n: integer;

begin

clrscr;

textcolor(15);

writeln(‘Nyuton usuli’); writeln;

write(‘boshlang’ich echim x0=’);

readln(x0); writeln;

write(‘taqribiy echim aniqligi eps=’);

readln(eps); writeln;

n:=0; x:=x0;

2: fx:=x*x-x-1;

f1x:=2*x-1;