| Jacobi矩阵特征值的并行算法 |
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| 引用本文： | 刘艳红,吕全义.Jacobi矩阵特征值的并行算法[J].纺织高校基础科学学报,2011,24(1):21-25. |
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| 作者姓名： | 刘艳红 吕全义 |
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| 作者单位： | 西北工业大学应用数学系; |
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| 基金项目： | 陕西省自然科学基金资助项目(2009JM1008) |
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| 摘 要： | 提出了并行求解实三对角矩阵特征值方法,该方法主要针对Jacobi矩阵.应用求多项式根的Sturm法,将矩阵特征多项式的求根区间隔离成单根区间;对已隔离出的单根区间先用二分法求解,达到一定精度后再用牛顿法精确求解.考虑到处理机负载平衡问题,将求根区间分成若干等分,然后按区间循环地将其分给各个处理机.各处理机并行地进行求根...
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| 关 键 词： | Jacobi矩阵 Sturm法 牛顿法 并行算法 并行效率 |
The parallel algorithm of eigenvalues of Jacobi matrix |
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| LIU Yan-hong,LV Quan-yi.The parallel algorithm of eigenvalues of Jacobi matrix[J].Basic Sciences Journal of Textile Universities,2011,24(1):21-25. |
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| Authors: | LIU Yan-hong LV Quan-yi |
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| Affiliation: | (Department of Applied Mathematics,Northwestern Polytechnical University,Xi′an 710129,China) |
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| Abstract: | A parallel algorithm for solving eigenvalues of real tridiagonal matrices is presented,which mainly apply to Jacobi matrices.This algorithm firstly isolates a small single region which only includes a root from the large region of roots of the polynomials by using the Sturm method;secondly looks for the accurate root by employing the Dichotomy and Newton iteration further.When considering the equally tasks among processors,the large region is divided into small regions,then these small regions are distribut... |
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| Keywords: | Jacobi matrix Sturm method Newton method parallel algorithm parallel efficiency |
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