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Консультация № 178211
04.05.2010, 23:37
45.00 руб.
06.05.2010, 21:57
0
4
1
Пусть А принадлежит R^(n*n), b принадлежит R^n. Доказать, что итерационная последовательность x^(k+1) = A*x^(k) + b, k = 1,2,...,x^(k) принадлежит R^n при любом начальном приближении сходиться к решению системы линейных алгебраических уравнений x = A*x + b тогда и только тогда, когда все собственные значения матрицы А по абсолютной величине меньше 1.
Обсуждение
05.05.2010, 09:06
общий
Рыбин Александр Андреевич:
Здравствуйте, Александр Андреевич!
К сожалению, условие задачи браузер не показывает. Может быть, приведете условие в мини-форуме в виде текста?
С уважением.
Здравствуйте, Александр Андреевич!
К сожалению, условие задачи браузер не показывает. Может быть, приведете условие в мини-форуме в виде текста?
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
05.05.2010, 15:31
общий
Пусть А принадлежит R^(n*n), b принадлежит R^n. Доказать, что итерационная последовательность x^(k+1) = A*x^(k) + b, k = 1,2,...,x^(k) принадлежит R^n при любом начальном приближении сходиться к решению системы линейных алгебраических уравнений x = A*x + b тогда и только тогда, когда все собственные значения матрицы А по абсолютной величине меньше 1.
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