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求解对称非线性矩阵特征值问题的一个三阶收敛的算法

陈广义,薛彦才   

  1. 中国科学院沈阳计算所 ;中国科学院沈阳计算所
  • 出版日期:1992-02-20 发布日期:1992-02-20

陈广义,薛彦才. 求解对称非线性矩阵特征值问题的一个三阶收敛的算法[J]. 数值计算与计算机应用, 1992, 13(2): 99-106.

A CUBICALLY CONVERGENT ALGORITHM FOR THE REAL SOLUTION OF THE GENERALIZED LATENT VALUE PROBLEM FOR SYMMETRIC FUNCTIONAL LAMBDA-MATRICES

  1. Chen Guang-yi;Xue Yan-cai Shenyang Institute of Computing Technology
  • Online:1992-02-20 Published:1992-02-20
考虑对称矩阵A(λ)∈R~(n×n),它的元素是λ的解析函数.求λ∈R,向量x≠0,使得求解(1.1)称为求解对称非线性矩阵特征值问题. 对于一般非线性矩阵特征值问题已经有了很多有效的方法.本文的目的是如何利用矩阵的对称性给出一个运算量与通常使用的二阶收敛方法的运算量相当的三阶收敛算法.
A cubically convergent algorithm is presented for solving the nonlinear eigenvalue problemA(λ)x= 0, x≠0, where A(λ) is a symmetric functional Lambda-matrix. The amount of com-putation is essentially the same as that of the usually used quadratically convergent algorithm,but the order of convergence is higher. What is more, this algorithm is better than Lancaster'scubically convergent algorithm. Numerical examples are also given.
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[6] A. Neumaier, Residual inverse iteration for the nonlinear eigenvalue problem,SIAM J.Numer.Anal,22(1985) , 914-923.
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