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Консультация № 180313
14.10.2010, 15:04
47.44 руб.
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1
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Здравствуйте .
Нужно написать универсальную прогроамму по методу ломаных.
Алгоритм:
1) находим константу Липшеца
2)вычислим x1z и p1z по формулам
x1z=(1/2L)*[f(a)-f(b)+L(a+b)
p1z=(1/2)*[f(a)+f(b)+L(a-b)
3) ДЕЛЬТА1=(1/2L)*[F(x1z)-p1z)
образуем две пары
(x1';p1) (x1'';p1) где
x1'=x1z-дельта 1
x1''=x1z+дельта 1
р1=(1/2)*[f(x1z)+p1z]
4)из полученных пар выбираем ту у которой вторая компонента минимальна
обозначим её (x2z;p2z) и исключим из рассм. множества.
Вместо этой пары добавим две новые пары
(x2';p2) (x2'';p2)
компоненты которых находим по формуле
дельта 2=(1/2L)(f(x2z)-p2z)
x2'=x2z-дельта 2
x2''=x2z+дельта 2
P2=(1/2)[f(x2z)+p2z]
в результате получим множество состоящее из трех пар чисел и т.д.
5)точность на каждом шаге определяется по формуле En=2L*дельта n
если точность достигнута то
xz=xnz
fz=f(xnz)
Нужно написать универсальную прогроамму по методу ломаных.
Алгоритм:
1) находим константу Липшеца
2)вычислим x1z и p1z по формулам
x1z=(1/2L)*[f(a)-f(b)+L(a+b)
p1z=(1/2)*[f(a)+f(b)+L(a-b)
3) ДЕЛЬТА1=(1/2L)*[F(x1z)-p1z)
образуем две пары
(x1';p1) (x1'';p1) где
x1'=x1z-дельта 1
x1''=x1z+дельта 1
р1=(1/2)*[f(x1z)+p1z]
4)из полученных пар выбираем ту у которой вторая компонента минимальна
обозначим её (x2z;p2z) и исключим из рассм. множества.
Вместо этой пары добавим две новые пары
(x2';p2) (x2'';p2)
компоненты которых находим по формуле
дельта 2=(1/2L)(f(x2z)-p2z)
x2'=x2z-дельта 2
x2''=x2z+дельта 2
P2=(1/2)[f(x2z)+p2z]
в результате получим множество состоящее из трех пар чисел и т.д.
5)точность на каждом шаге определяется по формуле En=2L*дельта n
если точность достигнута то
xz=xnz
fz=f(xnz)
Обсуждение
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