| 同伦方法求解混合三角多项式方程组 |
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| 引用本文： | 于妍,惠淑荣,鄢东姝.同伦方法求解混合三角多项式方程组[J].沈阳农业大学学报,2007,38(3):446-448. |
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| 作者姓名： | 于妍 惠淑荣 鄢东姝 |
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| 作者单位： | 1. 沈阳农业大学,基础部,沈阳,110161
2. 吉林建筑工程学院,基础部,长春,130021 |
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| 摘 要： | 解混合三角多项式方程组时,一般利用变元替换以及添加多个二次方程将原问题转化为不含三角函数的多项式方程组,然后求解,但这样会增大问题的规模导致计算量增大。利用同伦方法直接求解混合三角多项式方程组,不需要将原方程组进行转化,从而不会增大问题的规模,节省计算时间。
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| 关 键 词： | 混合三角多项式方程组 同伦方法 Bezout数 |
| 文章编号： | 1000-1700（2007）03-0446-03 |
| 修稿时间： | 2007-01-20 |
Standard Homotopy for Mixed Trigonometric Polynomial Systems |
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| YU Yan,HUI Shu-rong,YAN Dong-shu.Standard Homotopy for Mixed Trigonometric Polynomial Systems[J].Journal of Shenyang Agricultural University,2007,38(3):446-448. |
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| Authors: | YU Yan HUI Shu-rong YAN Dong-shu |
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| Institution: | 1. Department of Basic Sciences, Shenyang Agricultural University, Shenyang 110161, China; 2. Department of Basic Sciences, Jilin Institute of Architectural and Civil Engineering, Changchun 130021, China |
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| Abstract: | Commonly,mixed trigonometric polynomial systems are transformed into polynomial systems by variable substituting and adding some quadratic equations,and then solved by some solution method.However,transformation of a mixed trigonometric polynomial system into a polynomial system will increase the dimension of the system and hence induce extra computation.We consider solving the mixed trigonometric polynomial systems by homotopy method directly without transformation,thus the dimension of the system won't be increased and computational time can be saved. |
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| Keywords: | mixed trigonometric polynomial systems homotopy method Bezout number |
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