| GPSD迭代法和Jacobi迭代法的敛散关系 |
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| 引用本文： | 陈恒新.GPSD迭代法和Jacobi迭代法的敛散关系[J].数学的实践与认识,2012,42(2):171-176. |
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| 作者姓名： | 陈恒新 |
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| 作者单位： | 华侨大学数学科学学院,福建泉州,362021 |
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| 摘 要： | 证明了当Jacobi迭代矩阵B非负时,解线性方程组Ax=b(A为不可约矩阵)的GPSD迭代法(0＜ωi＜Ti≤1,i=1,2,…,n)和Jacobi迭代法同时敛散,给出了其谱半径p(ST,Ω)和ρ(B)之间的关系.
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| 关 键 词： | GPSD迭代法 Jacobi迭代法 收敛性 发散性 |
Convergent and Divergent Relation Between GPSD Iterative Method and Jacobi Method |
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| CHEN Heng-xin.Convergent and Divergent Relation Between GPSD Iterative Method and Jacobi Method[J].Mathematics in Practice and Theory,2012,42(2):171-176. |
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| Authors: | CHEN Heng-xin |
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| Institution: | CHEN Heng-xin (School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China) |
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| Abstract: | GPSD iterative method（0<ωi<τi≤1,i = 1,2,…,n）and Jacobi iterative method as the methods For solving linear equation system Ax=b（A is a irreduciable matrix） are proved to be convergent and divergent simultaneously in case Jacobi matrix B is nonnegative.The relation between their spectral radiusρ(SΤ,Ω) andρ（B）is given. |
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| Keywords: | GPSD iterative method Jacobi iterative method convergence divergence |
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