Предположим теперь, что относительно производной
![](data:image/gif;base64,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)
многочлена
![](data:image/gif;base64,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)
известны интервалы ее знакопостоянства, т.е. такие точки
![](data:image/gif;base64,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)
, что на участках
![](data:image/gif;base64,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)
функция
![](data:image/gif;base64,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)
знак не меняет, а проходя через каждую из точек
![](data:image/gif;base64,R0lGODlhEwAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAAPAAwAhQAAAAAAAB0AAB4eAB0AHQAAMwAdMx0dSAAdSAAzWx1GbB1IbjIAHTIAMjIyWjNZfzNdgDNbgEgcAEgdHVszAFozAFszM0gzSF13d1luf0huf11/f1VmZmxGHX9ZM39uSH9/XXtqRGZ3d2aIiIBbM4BdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY3QIBwSCwOBYEHIFAwEhkDocQp9BQV1CIh2xhWihfiQVhpZgNoJ2I4yRJD7iEFvXY64sJSYAEIAgA7)
меняет знак. Нетрудно обосновать в этой ситуации следующие выводы: 1) если внутри интервала (
-R,R) точек
![](data:image/gif;base64,R0lGODlhEwAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAAPAAwAhQAAAAAAAB0AAB4eAB0AHQAAMwAdMx0dSAAdSAAzWx1GbB1IbjIAHTIAMjIyWjNZfzNdgDNbgEgcAEgdHVszAFozAFszM0gzSF13d1luf0huf11/f1VmZmxGHX9ZM39uSH9/XXtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY2QIBwSCwOBYEHIFAwEhkDocQp9BQX1CIh2xhWihfiQVhpZgNoJ2I4yRJD7iEFvXY64kJSABsEADs=)
нет вообще и
![](data:image/gif;base64,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)
, то корней (напоминаем: вещественных!) у уравнения
![](data:image/gif;base64,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)
нет; если
![](data:image/gif;base64,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)
, то корень в интервале
![](data:image/gif;base64,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)
есть и его надо уточнить с заданной точностью; 2) если в интервале (
-R,R) точки
![](data:image/gif;base64,R0lGODlhEwAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAAPAAwAhQAAAAAAAB0AAB4eAB0AHQAAMwAdMx0dSAAdSAAzWx1GbB1IbjIAHTIAMjIyWjNZfzNdgDNbgEgcAEgdHVszAFozAFszM0gzSF13d1luf0huf11/f1VmZmxGHX9ZM39uSH9/XXtqRGZ3d2aIiIBbM4BdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY3QIBwSCwOBYEHIFAwEhkDocQp9BQV1CIh2xhWihfiQVhpZgNoJ2I4yRJD7iEFvXY64sJSYAEIAgA7)
оказались, то надо просчитать
![](data:image/gif;base64,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)
в этих точках и в точках
![](data:image/gif;base64,R0lGODlhHAAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAWAAwAhQAAAAAAAB0AAB0AHQAAHQAAMwAdSAAcSAAyWgAzWgAzWx1GbB1IbjMAADNbgEgcAEceM0geNFszAFozAF1/f113d0huf0Rqe2xGHW5IHX9/XXtqRH9uSHd3XXd3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZCQIBwSCwaj0iAJMAMGCFJ4aQgdEaPCWFjQYRGG0NBtdk8gqiAx/PaVFyN6vPRixxo38bDMIu/DwlDZGVEgwANAQpBADs=)
; если среди этих значений нуля нет и все они имеют один и тот же знак, то корней (напоминаем: вещественных!) уравнение
![](data:image/gif;base64,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)
не имеет; если же среди этих значений будут числа с разными знаками, то это позволит выделить все участки, на концах которых
![](data:image/gif;base64,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)
имеет разные знаки, а внутри которых
![](data:image/gif;base64,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)
знак не меняет. К каждому такому участку применима процедура уточнения корня (деление отрезка пополам, методы хорд и касательных).
И еще одно замечание. Если вещественные корни (все) уравнения
![](data:image/gif;base64,R0lGODlhPAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgA4AA8AhQAAAAAAAB4AHh0AHQAAHR0AAAAAMx0AMh0AMwAdSAAcSB0dSAAzWgAzWx1GbB1IbjMAADIAHTMAHTMAMzIAMjQ0HTNZfzNbgEgcAEgdAFozAFszAF1/f113d0huf0Rqe2xGHX9ZM25GM3d3XX9/XX9uSHtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwa2QIBwSCwaj8ikMgkJGCdJ6HIacCYjgFTRsBRMkykuAILUHCnfw/eIISqMITHRvGasi4NhaeAhZqpyQlhFAQRCKQEJQmp3h4FkRXRbRyAAlUSQQxtVnFUNk0MQF0WZQyCBRAVGEA6NQoGqRYygR6OYrkJ5Qnt9pm9FYUgVdrdEm52eRW1Dv0StRoNFrQsAIkOzjVpCpblIG8+WAZ8Af6bjuCBVRpdJH7jvpkIIXUui8EgBqPf7RUEAOw==)
известны, то по ним полностью восстанавливаются участки знакопостоянства функции
![](data:image/gif;base64,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)
: надо просчитать
![](data:image/gif;base64,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)
между любыми двумя соседними корнями и по совокупности знаков полученных чисел сделать вывод.
Процедуру выяснения участков знакопостоянства производной
![](data:image/gif;base64,R0lGODlhKQAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAjAA8AhQAAAAAAAB4AHgAAHR0AAB0AHQAAMx0AMx0AMgAdSAAcSB0dSAAzWgAzWx1GbB1IbjMAADIAHTMAHTMAMzIAMjMeRzQ0HTNbgEgcAEgdAFozAFszAEZGbl1/f113d0huf0Rqe2xGHX9ZM25GM3d3XX9/XX9uSHtqRHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwaGQIBwSCwaj8gjJEA0FCdJaBIQAayGmKJzKkhqjNkhZTo8HEVbYmX4JQ8ZxUwgkDZWi4GBUBRICBFGbUl1QyEAhkQQRopJIYRDBIsORYBTj0MXRYyFCmSXABZwiUaTU3dFDwALACNDlUMFbhulhwENQnKFt4VuQyC9QohmwF1TEJlCdMDLQ0EAOw==)
можно организовать так. Вычислим производные многочлена
![](data:image/gif;base64,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)
:
![](data:image/gif;base64,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)
; заметим, что производная
![](data:image/gif;base64,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)
- линейная функция. Поэтому участки ее знакопостоянства вычислимы. Если
![](data:image/gif;base64,R0lGODlhJQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAgAAwAhQAAAAAAAB0AABwcHAAAMx0dSAAdSAAzWgAzWx1GbDMAADMAHTIAHTIAMjNZfzNGbjNbgEgcAEgdAEgdHUceM1ozAFszAFozHVszM0hbSEhZf1l/WV1/f0huf2xGHX9ZM39ZSHd3XX9uSH9/XXtqRHd3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZQQIBwSCwaj8ikcqgIBBzL6NETkFqJkau2chAKAhCAJJDQFrPDBmBxtDjfTkT0BMAMO2ZkZTAs5JEKQx5HcG9HZUIaRQx/AHAEQogAAn+FQkEAOw==)
, то уже возможны формальные действия по описанной выше схеме по уточнению корней исходного уравнения. Если же
![](data:image/gif;base64,R0lGODlhJQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAgAAwAhQAAAAAAAB0AABwcHAAeHgAAMwAdSB0dSAAzWgAzWx1GbDMAADMAHTIAHTIAMjNZfzNGbjNbgEgcAEgdAEgdHUceM1ozAFozHVszM0hbSEhZf1l/WV1/f0huf2xGHX9ZM39ZSHd3XX9uSH9/XXtqRHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZaQIBwSCwaj8ikcrgIBB7L6NETkFqJkiviatkCBIEIYBJQFFEB7zI7dAAYy4DhigJghh2loCC1DIYHSwIEUgtDHkkkAnNIZkIaRQ1IckpOTnwAjl9HCXGWVQBBADs=)
, то решим по описанной выше схеме уравнение
![](data:image/gif;base64,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)
и по его корням установим участки знакопостоянства функции
![](data:image/gif;base64,R0lGODlhQAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgA7ABIAhgAAAAAAAB4AHgAAHR0AAB0AHR0AMwAAMx0AMh0dSAAdSB0zWgAyWgAzWgAzWx1IXx1GbB1IbjMAADMAHTIAHTIAMjMAMzQeSDQ0HTMzWzNGbjNZfzNbgDNdgEgdHUgdAEkdHUgcAEgeNEceM1ozHVozAFszAEgzM1oyMlszM0ZGRltISFV7VVl/WV13d11/f0huf0Rqe1VmZmxGHW5IHW5GM39ZM25ISHd3XX9/XX9uSHtqRHd3ZmaIiIBbM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwfXgACCg4SFhoeIiYqLiBeMABIBEAAij5aMI5cAFYIJmp+EPoM6ACwSk4gkgxygj5GJJ62EFoq0ihMAooKqhB0ADwABwoW+gguFNgeMAoklixEAKIkMtZYGh8mGugApghIKh8IBq4XQlg2FH8LKhSCtjoQUhgEDgwHgggiGzo2flaHsDKFzUEiCIYOyHgUsRAAVoVOF9CVcNGMhoRCHEA6agW+iIouCagBAV9CQOY+abCSSOKgAykUmCo0TpO7kDIIbXzLCpWmGoGs6FzFbJKFYMJBBD9l6FAgAOw==)
; затем решим по описанной выше схеме уравнение
![](data:image/gif;base64,R0lGODlhVwAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgBSABIAhQAAAAAAAB0AAB4AHh0AHQAAHR0AMgAAMx0AMx0dSAAdSAAcSAAzWh0zWgAzWx1GbB1IbjMAADIAHTMAHTMAMzIAMjQeSDMeRzQ0HTMzWzNGbjNZfzNbgEgdHUgdAEgcAEkdHUgeNEceM1szAFozHVozAEgzM1szM0ZGRltISEhZf1l/WV13d11/f0huf0Rqe2xGHW5IHW5GM39ZM3d3XX9uSH9/XXtqRGZ3d2aIiIBbM4BuboiIZgECAwECAwECAwb0QIBwSCwaj8ikcslsOok1QeBJrVZF1IswYe16iY+hARBJ3oawr7oZmQJkRRMgcxwFGEtKUq+GBdxIEgA6Rx2DQ3+ATAdLA18zjGRIJWspQxpFFU1jXR9EC0aQRmFEZUZ2gGlElE54VgRDNQQuRB5/kWtGgkUBBYgKQpxVuJJFrLlHxGgAqkOmQ6iJfw5FxBEcRc/IRDDKQwJGEaRUxOBFwttE3kPYpV2wQrK0aKDp1UgY4UbSiUYeG0OAFRlnT8iuIhAAcIETrAshIdqEwCsIZkiMANQA2Frm5aIiIc0oDpnwQmQSVQhMFnGkJGKuAOtUyiwSBAA7)
и по его корням определим участки знакопостоянства функции
![](data:image/gif;base64,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)
и так далее, пока не окажется решенным исходное уравнение
![](data:image/gif;base64,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)
.
Полученная в процессе решения информация позволяет установить также и кратность каждого корня уравнения
![](data:image/gif;base64,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)
; напомним, что
корень
уравнения
считается имеющим кратность ![](data:image/gif;base64,R0lGODlhDQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAJAAwAhQAAAAAAAB0AAB0AHQAAHR0AMgAAMx0dSAAcSAAzWwAyWh1GbB1IbjMAADIAHTMzWzNbgEgcAFozAFszAEhIW0huf11/f2xGHW5IHX9ZM39/XX9uSHd3XXtqRGZmVWaIiIiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwYqQIBwSAQ0AsWhIyk8MC9MIQQgCCCFhSegk5RYDcXlZlAZZoaRImMYIJSDADs=)
,
если ![](data:image/gif;base64,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)
,
но ![](data:image/gif;base64,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)
. В этом случае, как известно из алгебры, имеет место представление
![](data:image/gif;base64,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)
, где
![](data:image/gif;base64,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)
- многочлен степени
![](data:image/gif;base64,R0lGODlhJQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAhAAwAhQAAAAAAAB0AABwcHB0AHQAAHR0AMgAAMx0dSAAcSAAdSAAzWgAzWwAyWh1GbB1IbjMAADIAHTMAHTIAMjMzWzVIbjNbgEgdAEgcAEgdHVszAFozAFszM0ZZRkhIW1l/WUhuf11/f2xGHW5IHX9/XX9uSHd3XXtqRHd3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZWQIBwSCwaj8ikkggJLJ/JCHRaRFCvoqMgYAFcAo7rsLt1CicAiZhoOKoAnCGoGKjbzcPsybgZDK1iG3UHRRB5awBSJQRzR1Jib0IYRQ9DAoiVQgEFc0EAOw==)
.
Основная литература
1. Бахвалов Н., Жидков Н., Кобельков Г. Численные методы. – М. – СПб.: Физматлит, 2008.
2. Пирумов У.Г. Численные методы. – М.: Дрофа, 2009.
3. Поршнев С.В. Вычислительная математика. – СПб.: БХВ - Петербург, 2004.
Дополнительная литература
1. Бакушинский А.Б., Власов В.К. Элементы высшей математики и численных методов. – М.: Просвещение, 1968
2. Бутузов и др. Математический анализ в вопросах и задачах: Уч. пособие для вузов. – М.: Высшая школа, 2007.
3. Гусак А.А., Гусак Г.М. Справочник по высшей математике. - Минск, 2009.
4. Колесников А.И. Краткий курс математики для экономистов. - М.: ИНФА-М, 20009.
5. Понтрягин Л.С. Обыкновенные дифференциальные уравнения. – М.: Наука, 2004.
6. Фихтенгольц Г.М. Курс дифференциального и интегрального исчисления. - М.: Наука 1999.
Ковязина Елена Михайловна
Вычислительная математика
Методические указания
Ответственный за выпуск: Глушкова А.И.
Технический редактор: Кочуров М.Г.
Корректор: Журавлева О.Н.
Издательский орган ВСЭИ
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