Метод Гаусса с выбором главной переменной (практическая работа по компьютерной алгебре) Текст программы. #include #include #include #include const num = 4; int i, j, I, J; int c[num+1]; long double x[num+1]; long double max; long double A[num][num+1];
// ———————————————————- void max_el(int sr, int st) { max = A[num+1-sr][num+2-st]; I = num+1-sr; J = num+2-st; for (i = num+1-sr ; i { for (j = num+2-st ; j { if (fabs(A[i][j]) > fabs(max)) { max = A[i][j]; I = i; J = j; } } } cout
// ———————————————————- void print(int sr, int st) { cout int i, j; for (i = num+1-sr ; i { for (j = num+2-st ; j { if (A[i][j] else gotoxy(12*j + j, i+1); cout } } }
// —————————————————————– void preob(int S) { int i, j; long double temp; for (j = S; j for (i = S + 1; i { temp = A[i][S];
for (j = S; j }
// —————————————————————– void perestanovka(int sr, int st) { if (J ! = (num+1-sr)) { for (i = 1; i A[i][J] = A[i][J] + A[i][num+1-sr]; A[i][num+1-sr] = A[i][J] – A[i][num+1-sr]; A[i][J] = A[i][J] – A[i][num+1-sr]; } c[J] = c[J] + c[num+1-sr]; c[num+1-sr] = c[J] – c[num+1-sr]; c[J] = c[J] – c[num+1-sr]; } if (I ! = (num+2-st)) { for (j = 1; j A[I][j] = A[I][j] + A[num+2-st][j]; A[num+2-st][j] = A[I][j] – A[num+2-st][j]; A[I][j] = A[I][j] – A[num+2-st][j]; } } }
// —————————————————————– void otvet() { float temp; for (i=num; i>=1; i–) { temp = A[i][num+1]; for(j = num; j > i; j–) temp = temp – A[i][j]*x[j]; x[i] = temp/A[i][i]; } }
// —————————————————————– void interface() { clrscr(); print(num, num+1); cout for (i = 1; i }
// —————————————————————– void load_file() { char ch; ifstream in(“c: \\gauss\\mat. dat”); cout for (i = 1 ; i { c[i] = i; while (ch ! = ‘|’) in >> ch; ch = ‘q’; for (j = 1 ; j> A[i][j]; } }
// —————————————————————– void main() { clrscr(); load_file(); int g; for(g = num+1; g >= 3; g–) { interface(); max_el(g-1, g); getch(); perestanovka(g-1, g); interface(); getch(); preob(num+2-g); interface(); getch(); } clrscr(); print(num, num+1); otvet(); print(num, num+1); cout long double X[num]; for (i=1; i for (i=1; i getch(); } Тестовые задания. Задание №1 (найти неизвестные): 4. 24×1 + 2. 73×2 – 1. 55×3 = 1. 87 2. 34×1 + 1. 27×2 + 3. 15×3 = 2. 16 3. 05×1 – 1. 05×2 – 0. 63×3 = -1. 25 1. 1 Результат выполнения программы: x1 = – 0. 025461 x2 = 0. 915112 x3 = 0. 335678 1. 2 Расчёт погрешности вычисления:
4. 24*(- 0. 025461) + 2. 73*0. 915112 – 1. 55*0. 335678 = 1, 87000022 погрешность: 2, 2*10-7
2. 34*(- 0. 025461) + 1. 27*0. 915112 + 3. 15*0. 335678 = 2, 1599992 погрешность: 8, 0*10-7
3. 05*(- 0. 025461) – 1. 05*0. 915112 – 0. 63*0. 335678 = -1, 25000079 погрешность: 7, 9*10-7 средняя погрешность вычисления: 6, 0*10-7 Задание №2 (найти неизвестные): 3. 81×1 + 0. 25×2 + 1. 28×3 + (0. 75+a)x4 = 4. 21
2. 25×1 + 1. 32×2 + (4. 5+a)x3 + 0. 49×4 = 6. 47+b 5. 31×1 + (0. 28+a) x2 + 0. 98×3 + 1. 04×4 = 2. 38 (9. 39+a)x1 + 2. 45×2 + 3. 35×3 + 2. 28×4 = 10. 48+b a = (0, 1, 2, 3, 4) b = (0, 1, 2, 3, 4, 5) 2. 1 Таблица значений. a b Ответы: 0 0 X1 = -12. 660899 X2 = -16. 107649 X3 = 5. 273899 X4 = 66. 299137 1 X1 = -12. 132586 X2 = -14. 858407 X3 = 5. 186943 X4 = 63. 347289 2 X1 = -11. 604272 X2 = -13. 609166 X3 = 5. 099988 X4 = 60. 39544 3 X1 = -11. 075957 X2 = -12. 359925 X3 = 5. 013031 X4 = 57. 443595 4 X1 = -10. 547642 X2 = -11. 110685 X3 = 4. 926076 X4 = 54. 491746 5 X1 = -10. 019327 X2 = -9. 861445 X3 = 4. 839121 X4 = 51. 539901 1 0 X1 = 13. 959632 X2 = -39. 106359 X3 = 7. 324007 X4 = -27. 756765 1 X1 = 16. 668562 X2 = -46. 672114 X3 = 8. 73446 X4 = -33. 605312 2 X1 = 19. 377489 X2 = -54. 237864 X3 = 10. 144913 X4 = -39. 453861 3 X1 = 22. 086416 X2 = -61. 803618 X3 = 11. 555367 X4 = -45. 30241 4 X1 = 24. 795347 X2 = -69. 369373 X3 = 12. 96582 X4 = -51. 150959 5 X1 = 27. 504276 X2 = -76. 935127 X3 = 14. 376274 X4 = -56. 999508 2 0 X1 = 1. 033843 X2 = -1. 696273 X3 = 0. 997951 X4 = -0. 211727 1 X1 = 1. 191176 X2 = -2. 016845 X3 = 1. 183171 X4 = -0. 486773 2 X1 = 1. 348508 X2 = -2. 337417 X3 = 1. 36839 X4 = -0. 761819 3 X1 = 1. 505841 X2 = -2. 657989 X3 = 1. 55361 X4 = -1. 036865 4 X1 = 1. 663174 X2 = -2. 978561 X3 = 1. 73883 X4 = -1. 311911 5 X1 = 1. 820507 X2 = -3. 299134 X3 = 1. 92405 X4 = -1. 586957 3 0 X1 = 0. 772977 X2 = -0. 794749 X3 = 0. 762146 X4 = 0. 13016 1 X1 = 0. 872765 X2 = -0. 954303 X3 = 0. 902687 X4 = -0. 008559 2 X1 = 0. 972553 X2 = -1. 113856 X3 = 1. 043229 X4 = -0. 147278 3 X1 = 1. 072341 X2 = -1. 27341 X3 = 1. 18377 X4 = -0. 285998 4 X1 = 1. 172129 X2 = -1. 432964 X3 = 1. 324311 X4 = -0. 424717 5 X1 = 1. 271917 X2 = -1. 592518 X3 = 1. 464853 X4 = -0. 563436 4 0 X1 = 0. 675128 X2 = -0. 476895 X3 = 0. 645225 X4 = 0. 196021 1 X1 = 0. 754634 X2 = -0. 580642 X3 = 0. 763131 X4 = 0. 105936 2 X1 = 0. 83414 X2 = -0. 68439 X3 = 0. 881037 X4 = 0. 015852 3 X1 = 0. 913647 X2 = -0. 788137 X3 = 0. 998942 X4 = -0. 074233 4 X1 = 0. 993153 X2 = -0. 891884 X3 = 1. 116848 X4 = -0. 164317 5 X1 = 1. 072659 X2 = -0. 995631 X3 = 1. 234754 X4 = -0. 254402