Ітераційний метод розв’язування системи поліноміальних рівнянь другого степеня
Systems of nonlinear algebraic equations have a wide application. As a rule, such systems aresolved using some iterative methods, which are based on the nonlinear functional expansion in aTaylor series in the neighborhood of the solution. However, these methods require giving theinitial approximatio...
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| Date: | 2019 |
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| Main Author: | |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2019
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| Subjects: | |
| Online Access: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/101 |
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| Journal Title: | Physico-mathematical modeling and informational technologies |
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Physico-mathematical modeling and informational technologies| Summary: | Systems of nonlinear algebraic equations have a wide application. As a rule, such systems aresolved using some iterative methods, which are based on the nonlinear functional expansion in aTaylor series in the neighborhood of the solution. However, these methods require giving theinitial approximation with sufficient accuracy, moreover, it is practically impossible to verify theconditions of the convergence beforehand. This paper suggests a new perspective method forsolving systems of polynomial equations of the second degree with many unknowns. Recurrencerelations for finding approximate solutions of polynomial equations over the field of real numbersare obtained. The convergence of operator continued fractions used in the computational schemeis investigated and some of their properties are shown. The numerical experiments confirming theefficiency of the method proposed have been conducted. |
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