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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: нужно реализовать решение заданной СЛАУ, учитывая тот факт, что на главной диагонали матрицы могут присутствовать нули. Решить методом Гаусса, матрицу выводить из файла заранее спасибо!
Обсуждение
Неизвестный
17.09.2011, 16:26
общий
Для исключения влияния нулей на главной диагонали, нужно сделать перестановку строк в матрице коэффициентов ( чтобы на диагональной позиции не было нулей) и не забыть о перестановке в векторе свободных членов.
Поэтому я не оформлял ответ, а лишь написал сообщение в мини-форум. Конечно, там надо малость переделать и доработать. Но практически затруднения минимальны -- я бы советовал вам попытаться. Если у меня найдётся время -- попробую сделать. Пока времени заняться вашей задачей нет.
var a,aa:array[1..n,1..n] of real; b,x:array[1..n] of real; i,j,k:integer; h:real; fa,fb:text;
begin {Считывание матрицы A} assign(fa,'a.txt'); reset(fa); for i:=1 to n do begin for j:=1 to n do read(fa,a[i,j]); readln(fa); end; close(fa); {Копия матрицы для проверки} aa:=a;
{Считывание вектора B} assign(fb,'b.txt'); reset(fb); for i:=1 to n do readln(fb,b[i]); close(fb); bb:=b;
{Прямой ход - исключение переменных} for i:=1 to n-1 do begin j:=i; {Перестановка строк при нулевом диагональном элементе} while (a[j,i]=0) and (j<=n) do inc(j); if j<>i then begin for k:=1 to n do begin h:=a[i,k]; a[i,k]:=a[j,k]; a[j,k]:=h; end; h:=b[i]; b[i]:=b[j]; b[j]:=h; end; {Обнуление поддиагональных коэффициентов A} for j:=i+1 to n do begin a[j,i]:=-a[j,i]/a[i,i]; for k:=i+1 to n do a[j,k]:=a[j,k]+a[j,i]*a[i,k]; b[j]:=b[j]+a[j,i]*b[i] end; end;
{Обратный ход - нахождение корней} for i:=n downto 1 do begin h:=b[i]; for j:=i+1 to n do h:=h-x[j]*a[i,j]; x[i]:=h/a[i,i] end;
writeln('Ответ: X='); for i:=1 to n do writeln(x[i]:0:3);
writeln('Проверка: A*x='); for i:=1 to n do begin b[i]:=0; for j:=1 to n do b[i]:=b[i]+aa[i,j]*x[j]; writeln(b[i]:0:3); end; readln;
end.[/code]
Исходный файл с матрицей A -- a.txt
Код:
1 2 3 4 5 5 4 3 2 1 3 2 4 1 5 5 5 1 1 2 2 2 3 3 4
Исходный файл с вектором b -- b.txt
Код:
10 11 12 13 14
Результат выполнения:
Код:
Ответ: X= 15.200 -14.000 -8.900 6.500 4.700
Проверка: A*x= 10.000 11.000 12.000 13.000 14.000
5
Спасибо большое!!
Форма ответа
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