| Applications of interval arithmetic in solving polynomial equations by Wu's elimination method |
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| 作者姓名： | CHEN Falai & YANG Wu |
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| 作者单位： | CHEN Falai & YANG Wu Department of Mathematics，University of Science and Technology of China，Hefei 230026，China |
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| 基金项目： | 国家杰出青年科学基金，国家重点基础研究发展计划(973计划)，the TRAPOYT in Higher Education Institutions of MOE of China Funds |
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| 摘 要： | Wu's elimination method is an important method for solving multivariate poly- nomial equations.In this paper,we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- tions.Parallel results such as zero-decomposition theorem are obtained for interval poly- nomial equations.The advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely overcome.Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved.Some examples are provided to illustrate the effectiveness of the proposed algorithm.
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Applications of interval arithmetic in solving polynomial equations by Wu’s elimination method |
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| CHEN Falai & YANG Wu.Applications of interval arithmetic in solving polynomial equations by Wu''''s elimination method[J].Science in China(Mathematics),2005,48(9):1260-1273. |
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| Authors: | CHEN Falai YANG Wu |
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| Institution: | Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
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| Abstract: | Wu's elimination method is an important method for solving multivariate poly- nomial equations.In this paper,we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- tions.Parallel results such as zero-decomposition theorem are obtained for interval poly- nomial equations.The advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely overcome.Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved.Some examples are provided to illustrate the effectiveness of the proposed algorithm. |
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| Keywords: | mathematical mechanization Wu's method polynomial equation interval arithmetic |
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