O'ZBЕKISTON RESPUBLIKASI AXBOROT TEXNOLOGIYALARI VA KOMMUNIKATSIYALARINI RIVOJLANTIRISH VAZIRLIGI MUHAMMAD AL-XORAZMIY NOMIDAGI TOSHKЕNT AXBOROT TЕXNOLOGIYALARI UNIVЕRSITЕTI
KOMPYUTER INJINIRINGI FAKULTET Axborot texnologiyalari kafedrasi
217-guruh talabasi Asadov G’ofurjonnig Algoritmlarni loyixalash fanidan
Labaratoriya ishi №1
Toshkent- 2021
Variant 14
1-topshiriq
(nxm) o’lchamdagi ikki o’lchovli A massiv berilgan, matritsaning har bir ustinidagi musbat elementlari yig’indisidan tashkil topgan bir o’lchovli massiv hosil qiling
Matematik modeli
m
Bi =∑sum, Ai j < 0 sum=1 i = 1..n
J=1
Model asosida masalani yechish algoritmi
Dastur kodi
Natija
Satrlar sonini kiriting = 4
Ustunlar sonini kiriting = 4
Massiv elementlarini kiritish
-1
-2
3
-5
1
-7
-6
-8
1
3
-5
7
8
9
10
-10
[10,12,13,7]
Process finished with exit code 0
2-Topshiriq
Berilgan integral qiymatini to‘g‘ri to‘rtburchaklar, trapetsiyalar va Simpson usullarida hisoblansin. (n=100 qiymatda natija olinsin). Har bir usul bo‘yicha har 10 qadamda n - qiymatda olingan natijalar quyidagi jadvalga to’ldirilib tahlil qilinsin.
n
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10
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20
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30
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40
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50
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60
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70
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80
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90
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100
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Integral yeg’indi
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To’g’ri to’rtburchaklar usuli
Xi
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5,2
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5,1
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5,06
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5,05
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5,04
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5,03
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5,02
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5,02
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5,02
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5,02
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n
∑h*f(xi)
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f(xi)
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218,12
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384,33
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551.94
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719.91
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888.02
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1056.20
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1224,42
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1392.67
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1560,94
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1729.21
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i=1
|
h* f(xi)
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87,25
|
7686
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73.59
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71.99
|
71.04
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70,41
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69,96
|
69.63
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69.37
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69.16
|
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Trapetsiyalar usuli
Xi
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4,6
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4,8
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4,86
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4,9
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4,92
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4,93
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4,94
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4,95
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4,95
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4.96
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n
∑ h*f(xi)
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f(xi)
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52,61
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69,47
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76,25
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79,89
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82,16
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83,7
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84,83
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85,68
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86,35
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86.89
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i=1
|
S
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69,03
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67,75
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67,52
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67,43
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67,39
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67,37
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67,36
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67,35
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67.35
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67.34
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Simpson usuli
Xi
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n
∑ h*f(xi)
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f(xi) / yi
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|
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i=1
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h* f(xi)
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|
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To’g’ri Tortburchaklar usuli Dastur kodi
import java.util.Scanner;
import static java.lang.Math.*;
public class Algo2 {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
//System.out.println("a ni kiriting ");
double a= PI;
//System.out.println("b ni kiriting ");
double b= PI*2;
// System.out.println("n ni kiriting ");
//double n = sc.nextDouble();
for (int n = 10; n <=100 ; n+=10) {
double S = 0;
double I;
double h = (b - a) / n;
for (double i = 1; i <= n; i++) {
S += f(a + i * h + h / 2);
}
I = h * S;
System.out.println("N = " +n);
System.out.println("xi = " + (a + n * h + h / 2));
System.out.println("f(xi) = " + abs(S));
System.out.println("h*f(xi) = " + abs(I));
System.out.println("*****************************************************************");
}
}
public static double f (double x){
return (1-cos(x))/pow((x-sin(x)),2);
}
}
Natija
Trapetsiya usuli
Dastur kodi
import java.util.Scanner;
import static java.lang.Math.*;
import static java.lang.Math.cos;
public class Algo2_2 {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
// System.out.println("a ni kiriting ");
double a = PI;
//System.out.println("b ni kiriting ");
double b= PI*2;
// System.out.println("n ni kiriting ");
//double n = sc.nextDouble();
for (int n = 10; n <=100 ; n+=10) {
double S = 0;
double I, x = 0;
double h = (b - a) / n;
for (double i = 0; i < n; i++) {
S += ((f(a + i * h) + f((a + i * h) + h)) / 2);
x = a + i * h;
}
I = h * S;
System.out.println("N = " +n);
System.out.println("xi = " + (a + n * h + h / 2));
System.out.println("f(xi) = " + abs(S));
System.out.println("h*f(xi) = " + abs(I));
System.out.println("***********************************************************");
}
}
public static double f (double x){
return (1-cos(x))/pow((x-sin(x)),2);
}
}
Natija
3-Topshiriq
Berilgan algebraik va transsendent tenglamalarni yechishda oraliqni teng ikkiga bo‘lish va vatarlar usullaridan foydalanib tenglamaning taqribiy ildizini 0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001 aniqliklarda hisoblansin. Olingan natijalar quyidagi jadvalga to’ldirilib tahlil qilinsin.
Usul e=
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0.1
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0.01
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0.001
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0.0001
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0.00001
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0.000001
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Kesmani 2 ga bo’lish
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Vatarlar
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Nyuton(urunma)
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